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Algebra 1

2.9.2 Graphing Inequalities

Algebra 12.9.2 Graphing Inequalities

2.9.2 Graphing Inequalities

2.9.2 • Graphing Inequalities

Activity

Work with a partner to match each of the following inequalities to its correct number line.

1.

  1. x<2

  2. x≥2

  3. x>2

  4. x≤2

2.

  1. x<2

  2. x≥2

  3. x>2

  4. x≤2

3.

  1. x<2

  2. x≥2

  3. x>2

  4. x≤2

4.

  1. x<2

  2. x≥2

  3. x>2

  4. x≤2

Why Should I Care?

Nafy Flatley has worked to achieve her goal of bringing the food of Senegal to the world through her snack mix company, TERANGA.

Coming up with snack mixes is not as simple as just combining ingredients. They have a lot of things to consider: What ingredients will they use? How much does each ingredient cost? What are the nutrititional values of each ingredient? How much does each ingredient weigh?

If they can translate each question in a linear inequality, then they can use math to find mixes that meet their goals.

Self Check

Which number line is represented by the inequality x ≥ – 4 ?

Additional Resources

Graphing Linear Inequalities

What number would make the inequality x > 3 x > 3 true? Are you thinking, “ x x could be 4”? That’s correct, but x x could be 6, too, or 37, or even 3.001. Any number greater than 3 is a solution to the inequality x > 3 x > 3 . We show all the solutions to the inequality x > 3 x > 3 on the number line by shading in all the numbers to the right of 3, to show that all numbers greater than 3 are solutions. Because the number 3 itself is not a solution, we put an open circle at 3.

We can also represent inequalities using interval notation. There is no upper end to the solution to this inequality. In interval notation, we express x > 3 x > 3 as ( 3 , ∞ ) ( 3 , ∞ ) . The symbol ∞ is read as “infinity.” It is not an actual number.

The figure below shows both the number line and the interval notation.

The inequality x ≤ 1 x ≤ 1 means all numbers less than or equal to 1. Here we need to show that 1 is a solution, too. We do that by putting a closed circle at x = 1 x = 1 . We then shade in all the numbers to the left of 1, to show that all numbers less than 1 are solutions. See the figure below.

There is no lower end to those numbers. We write x ≤ 1 x ≤ 1 in interval notation as ( − ∞ , 1 ] ( − ∞ , 1 ] . The symbol − ∞ ∞ is read as “negative infinity.” The figure below shows both the number line and interval notation.

Inequalities, Number Lines, and Interval Notation

Try it

Graphing Linear Inequalities

For questions 1 – 2 use the following inequality:

x > − 3 x > − 3
1.

Write the inequality on a number line.

2.

Write the inequality in interval notation.

For questions 3 and 4 use the following inequality:

x ≤ 5 x ≤ 5
3.

Write the inequality in interval notation.

4.

Write the inequality on a number line.

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