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Elementary Algebra 2e

4.7 Graphs of Linear Inequalities

Elementary Algebra 2e4.7 Graphs of Linear Inequalities
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index
Be Prepared 4.15

Before you get started, take this readiness quiz.

Solve: 4x+3>234x+3>23.
If you missed this problem, review Example 2.73.

Be Prepared 4.16

Translate from algebra to English: x<5x<5.
If you missed this problem, review Example 1.12.

Be Prepared 4.17

Evaluate 3x2y3x2y when x=1x=1, y=−2y=−2.
If you missed this problem, review Example 1.55.

Verify Solutions to an Inequality in Two Variables

We have learned how to solve inequalities in one variable. Now, we will look at inequalities in two variables. Inequalities in two variables have many applications. If you ran a business, for example, you would want your revenue to be greater than your costs—so that your business would make a profit.

Linear Inequality

A linear inequality is an inequality that can be written in one of the following forms:

Ax+By>CAx+ByCAx+By<CAx+ByCAx+By>CAx+ByCAx+By<CAx+ByC

where AandBAandB are not both zero.

Do you remember that an inequality with one variable had many solutions? The solution to the inequality x>3x>3 is any number greater than 3. We showed this on the number line by shading in the number line to the right of 3, and putting an open parenthesis at 3. See Figure 4.30.

The figure shows a number line extending from negative 5 to 5. A parenthesis is shown at positive 3 and an arrow extends form positive 3 to positive infinity.
Figure 4.30

Similarly, inequalities in two variables have many solutions. Any ordered pair (x,y)(x,y) that makes the inequality true when we substitute in the values is a solution of the inequality.

Solution of a Linear Inequality

An ordered pair (x,y)(x,y) is a solution of a linear inequality if the inequality is true when we substitute the values of x and y.

Example 4.69

Determine whether each ordered pair is a solution to the inequality y>x+4y>x+4:

(0,0)(0,0) (1,6)(1,6) (2,6)(2,6) (−5,−15)(−5,−15) (−8,12)(−8,12)

Try It 4.137

Determine whether each ordered pair is a solution to the inequality y>x3y>x3:

(0,0)(0,0) (4,9)(4,9) (−2,1)(−2,1) (−5,−3)(−5,−3) (5,1)(5,1)

Try It 4.138

Determine whether each ordered pair is a solution to the inequality y<x+1y<x+1:

(0,0)(0,0) (8,6)(8,6) (−2,−1)(−2,−1) (3,4)(3,4) (−1,−4)(−1,−4)

Recognize the Relation Between the Solutions of an Inequality and its Graph

Now, we will look at how the solutions of an inequality relate to its graph.

Let’s think about the number line in Figure 4.30 again. The point x=3x=3 separated that number line into two parts. On one side of 3 are all the numbers less than 3. On the other side of 3 all the numbers are greater than 3. See Figure 4.31.

The figure shows a number line extending from negative 5 to 5. A parenthesis is shown at positive 3 and an arrow extends form positive 3 to positive infinity. An arrow above the number line extends from 3 and points to the left. It is labeled “numbers less than 3.” An arrow above the number line extends from 3 and points to the right. It is labeled “numbers greater than 3.”
Figure 4.31

The solution to x>3x>3 is the shaded part of the number line to the right of x=3x=3.

Similarly, the line y=x+4y=x+4 separates the plane into two regions. On one side of the line are points with y<x+4y<x+4. On the other side of the line are the points with y>x+4y>x+4. We call the line y=x+4y=x+4 a boundary line.

Boundary Line

The line with equation Ax+By=CAx+By=C is the boundary line that separates the region where Ax+By>CAx+By>C from the region where Ax+By<CAx+By<C.

For an inequality in one variable, the endpoint is shown with a parenthesis or a bracket depending on whether or not aa is included in the solution:

The figure shows two number lines. The number line on the left is labeled x is less than a. The number line shows a parenthesis at a and an arrow that points to the left. The number line on the right is labeled x is less than or equal to a. The number line shows a bracket at a and an arrow that points to the left.

Similarly, for an inequality in two variables, the boundary line is shown with a solid or dashed line to indicate whether or not it the line is included in the solution. This is summarized in Table 4.48

Ax+By<CAx+By<C Ax+ByCAx+ByC
Ax+By>CAx+By>C Ax+ByCAx+ByC
Boundary line is not included in solution. Boundary line is included in solution.
Boundary line is dashed. Boundary line is solid.
Table 4.48

Now, let’s take a look at what we found in Example 4.69. We’ll start by graphing the line y=x+4y=x+4, and then we’ll plot the five points we tested. See Figure 4.32.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x plus 4 is plotted as an arrow extending from the bottom left toward the upper right. The following points are plotted and labeled (negative 8, 12), (1, 6), (2, 6), (0, 0), and (negative 5, negative 15).
Figure 4.32

In Example 4.69 we found that some of the points were solutions to the inequality y>x+4y>x+4 and some were not.

Which of the points we plotted are solutions to the inequality y>x+4y>x+4? The points (1,6)(1,6) and (−8,12)(−8,12) are solutions to the inequality y>x+4y>x+4. Notice that they are both on the same side of the boundary line y=x+4y=x+4.

The two points (0,0)(0,0) and (−5,−15)(−5,−15) are on the other side of the boundary line y=x+4y=x+4, and they are not solutions to the inequality y>x+4y>x+4. For those two points, y<x+4y<x+4.

What about the point (2,6)(2,6)? Because 6=2+46=2+4, the point is a solution to the equation y=x+4y=x+4. So the point (2,6)(2,6) is on the boundary line.

Let’s take another point on the left side of the boundary line and test whether or not it is a solution to the inequality y>x+4y>x+4. The point (0,10)(0,10) clearly looks to be to the left of the boundary line, doesn’t it? Is it a solution to the inequality?

y>x+410>?0+410>4So,(0,10)is a solution toy>x+4.y>x+410>?0+410>4So,(0,10)is a solution toy>x+4.

Any point you choose on the left side of the boundary line is a solution to the inequality y>x+4y>x+4. All points on the left are solutions.

Similarly, all points on the right side of the boundary line, the side with (0,0)(0,0) and (−5,−15)(−5,−15), are not solutions to y>x+4y>x+4. See Figure 4.33.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x plus 4 is plotted as an arrow extending from the bottom left toward the upper right. The following points are plotted and labeled (negative 8, 12), (1, 6), (2, 6), (0, 0), and (negative 5, negative 15). To the upper left of the line is the inequality y is greater than x plus 4. To the right of the line is the inequality y is less than x plus 4.
Figure 4.33

The graph of the inequality y>x+4y>x+4 is shown in Figure 4.34 below. The line y=x+4y=x+4 divides the plane into two regions. The shaded side shows the solutions to the inequality y>x+4y>x+4.

The points on the boundary line, those where y=x+4y=x+4, are not solutions to the inequality y>x+4y>x+4, so the line itself is not part of the solution. We show that by making the line dashed, not solid.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x plus 4 is plotted as a dashed arrow extending from the bottom left toward the upper right. The coordinate plane to the upper left of the line is shaded.
Figure 4.34 The graph of the inequality y>x+4y>x+4.

Example 4.70

The boundary line shown is y=2x1y=2x1. Write the inequality shown by the graph.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 2 x minus 1 is plotted as a solid arrow extending from the bottom left toward the upper right. The coordinate plane to the left of the line is shaded
Try It 4.139

Write the inequality shown by the graph with the boundary line y=−2x+3y=−2x+3.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 2 x plus 3 is plotted as a solid arrow extending from the top left toward the bottom right. The coordinate plane to the right of the line is shaded.
Try It 4.140

Write the inequality shown by the graph with the boundary line y=12x4y=12x4.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals one half x minus 4 is plotted as a solid arrow extending from the bottom left toward the top right. The coordinate plane to the bottom right of the line is shaded.

Example 4.71

The boundary line shown is 2x+3y=62x+3y=6. Write the inequality shown by the graph.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x plus 3 y equals 6 is plotted as a dashed arrow extending from the top left toward the bottom right. The coordinate plane to the bottom of the line is shaded.
Try It 4.141

Write the inequality shown by the shaded region in the graph with the boundary line x4y=8x4y=8.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus 4 y equals 8 is plotted as a solid arrow extending from the bottom left toward the top right. The coordinate plane to the top of the line is shaded.
Try It 4.142

Write the inequality shown by the shaded region in the graph with the boundary line 3xy=63xy=6.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 3 x minus y equals 6 is plotted as a solid arrow extending from the bottom left toward the top right. The coordinate plane to the right of the line is shaded.

Graph Linear Inequalities

Now, we’re ready to put all this together to graph linear inequalities.

Example 4.72

How to Graph Linear Inequalities

Graph the linear inequality y34x2y34x2.

Try It 4.143

Graph the linear inequality y52x4y52x4.

Try It 4.144

Graph the linear inequality y23x5y23x5.

The steps we take to graph a linear inequality are summarized here.

How To

Graph a linear inequality.

  1. Step 1. Identify and graph the boundary line.
    • If the inequality is oror, the boundary line is solid.
    • If the inequality is < or >, the boundary line is dashed.
  2. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality?
  3. Step 3. Shade in one side of the boundary line.
    • If the test point is a solution, shade in the side that includes the point.
    • If the test point is not a solution, shade in the opposite side.

Example 4.73

Graph the linear inequality x2y<5x2y<5.

Try It 4.145

Graph the linear inequality 2x3y62x3y6.

Try It 4.146

Graph the linear inequality 2xy>32xy>3.

What if the boundary line goes through the origin? Then we won’t be able to use (0,0)(0,0) as a test point. No problem—we’ll just choose some other point that is not on the boundary line.

Example 4.74

Graph the linear inequality y−4xy−4x.

Try It 4.147

Graph the linear inequality y>−3xy>−3x.

Try It 4.148

Graph the linear inequality y−2xy−2x.

Some linear inequalities have only one variable. They may have an x but no y, or a y but no x. In these cases, the boundary line will be either a vertical or a horizontal line. Do you remember?

x=avertical liney=bhorizontal linex=avertical liney=bhorizontal line

Example 4.75

Graph the linear inequality y>3y>3.

Try It 4.149

Graph the linear inequality y<5y<5.

Try It 4.150

Graph the linear inequality y−1y−1.

Section 4.7 Exercises

Practice Makes Perfect

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

504.

Determine whether each ordered pair is a solution to the inequality y>x1y>x1:

  1. (0,1)(0,1)
  2. (−4,−1)(−4,−1)
  3. (4,2)(4,2)
  4. (3,0)(3,0)
  5. (−2,−3)(−2,−3)
505.

Determine whether each ordered pair is a solution to the inequality y>x3y>x3:

  1. (0,0)(0,0)
  2. (2,1)(2,1)
  3. (−1,−5)(−1,−5)
  4. (−6,−3)(−6,−3)
  5. (1,0)(1,0)
506.

Determine whether each ordered pair is a solution to the inequality y<x+2y<x+2:

  1. (0,3)(0,3)
  2. (−3,−2)(−3,−2)
  3. (−2,0)(−2,0)
  4. (0,0)(0,0)
  5. (−1,4)(−1,4)
507.

Determine whether each ordered pair is a solution to the inequality y<x+5y<x+5:

  1. (−3,0)(−3,0)
  2. (1,6)(1,6)
  3. (−6,−2)(−6,−2)
  4. (0,1)(0,1)
  5. (5,−4)(5,−4)
508.

Determine whether each ordered pair is a solution to the inequality x+y>4x+y>4:

  1. (5,1)(5,1)
  2. (−2,6)(−2,6)
  3. (3,2)(3,2)
  4. (10,−5)(10,−5)
  5. (0,0)(0,0)
509.

Determine whether each ordered pair is a solution to the inequality x+y>2x+y>2:

  1. (1,1)(1,1)
  2. (4,−3)(4,−3)
  3. (0,0)(0,0)
  4. (−8,12)(−8,12)
  5. (3,0)(3,0)

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

510.

Write the inequality shown by the graph with the boundary line y=3x4.y=3x4.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 3x minus 4 is plotted as a dashed line extending from the bottom left toward the top right. The region to the right of the line is shaded.
511.

Write the inequality shown by the graph with the boundary line y=2x4.y=2x4.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 2x minus 4 is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.
512.

Write the inequality shown by the graph with the boundary line y=12x+1.y=12x+1.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative one-half x plus 1 is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.
513.

Write the inequality shown by the graph with the boundary line y=13x2.y=13x2.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative one-third x minus 2 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
514.

Write the inequality shown by the shaded region in the graph with the boundary line x+y=5.x+y=5.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x plus y equals 5 is plotted as a solid line extending from the top left toward the bottom right. The region above the line is shaded.
515.

Write the inequality shown by the shaded region in the graph with the boundary line x+y=3.x+y=3.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x plus y equals 3 is plotted as a solid line extending from the top left toward the bottom right. The region above the line is shaded.
516.

Write the inequality shown by the shaded region in the graph with the boundary line 2x+y=−4.2x+y=−4.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x plus y equals negative 4 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
517.

Write the inequality shown by the shaded region in the graph with the boundary line x+2y=−2.x+2y=−2.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x plus 2 y equals negative 2 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.
518.

Write the inequality shown by the shaded region in the graph with the boundary line 3xy=6.3xy=6.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 3 x minus y equals 6 is plotted as a dashed line extending from the bottom left toward the top right. The region to the left of the line is shaded.
519.

Write the inequality shown by the shaded region in the graph with the boundary line 2xy=4.2xy=4.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x minus y equals 4 is plotted as a dashed line extending from the bottom left toward the top right. The region to the left of the line is shaded.
520.

Write the inequality shown by the shaded region in the graph with the boundary line 2x5y=10.2x5y=10.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x minus 5 y equals 10 is plotted as a dashed line extending from the bottom left toward the top right. The region below the line is shaded.
521.

Write the inequality shown by the shaded region in the graph with the boundary line 4x3y=12.4x3y=12.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 4 x minus 3 y equals 12 is plotted as a dashed line extending from the bottom left toward the top right. The region below the line is shaded.

Graph Linear Inequalities

In the following exercises, graph each linear inequality.

522.

Graph the linear inequality y>23x1y>23x1.

523.

Graph the linear inequality y<35x+2y<35x+2.

524.

Graph the linear inequality y12x+4y12x+4.

525.

Graph the linear inequality y13x2y13x2.

526.

Graph the linear inequality xy3xy3.

527.

Graph the linear inequality xy−2xy−2.

528.

Graph the linear inequality 4x+y>−44x+y>−4.

529.

Graph the linear inequality x+5y<−5x+5y<−5.

530.

Graph the linear inequality 3x+2y−63x+2y−6.

531.

Graph the linear inequality 4x+2y−84x+2y−8.

532.

Graph the linear inequality y>4xy>4x.

533.

Graph the linear inequality y>xy>x.

534.

Graph the linear inequality yxyx.

535.

Graph the linear inequality y−3xy−3x.

536.

Graph the linear inequality y−2y−2.

537.

Graph the linear inequality y<−1y<−1.

538.

Graph the linear inequality y<4y<4.

539.

Graph the linear inequality y2y2.

540.

Graph the linear inequality x5x5.

541.

Graph the linear inequality x>−2x>−2.

542.

Graph the linear inequality x>−3x>−3.

543.

Graph the linear inequality x4x4.

544.

Graph the linear inequality xy<4xy<4.

545.

Graph the linear inequality xy<−3xy<−3.

546.

Graph the linear inequality y32xy32x.

547.

Graph the linear inequality y54xy54x.

548.

Graph the linear inequality y>−2x+1y>−2x+1.

549.

Graph the linear inequality y<−3x4y<−3x4.

550.

Graph the linear inequality x−1x−1.

551.

Graph the linear inequality x0x0.

Everyday Math

552.

Money. Gerry wants to have a maximum of $100 cash at the ticket booth when his church carnival opens. He will have $1 bills and $5 bills. If x is the number of $1 bills and y is the number of $5 bills, the inequality x+5y100x+5y100 models the situation.

  1. Graph the inequality.
  2. List three solutions to the inequality x+5y100x+5y100 where both x and y are integers.
553.

Shopping. Tula has $20 to spend at the used book sale. Hardcover books cost $2 each and paperback books cost $0.50 each. If x is the number of hardcover books Tula can buy and y is the number of paperback books she can buy, the inequality 2x+12y202x+12y20 models the situation.

  1. Graph the inequality.
  2. List three solutions to the inequality 2x+12y202x+12y20 where both x and y are whole numbers.

Writing Exercises

554.

Lester thinks that the solution of any inequality with a > sign is the region above the line and the solution of any inequality with a < sign is the region below the line. Is Lester correct? Explain why or why not.

555.

Explain why in some graphs of linear inequalities the boundary line is solid but in other graphs it is dashed.

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has four rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “verify solutions to an inequality in two variables,”, “recognize the relation between the solutions of an inequality and its graph,” and “graph linear inequalities.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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