College Algebra with Corequisite Support

# 2.2Linear Equations in One Variable

College Algebra with Corequisite Support2.2 Linear Equations in One Variable

### Corequisite Skills

#### Learning Objectives

• Simplify expressions using order of operations (IA 1.1.3)
• Solve linear equations using a general strategy (IA 2.1.1)

### How To

#### Use the order of operations

1. Step 1. Parentheses and Other Grouping Symbols
• Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
2. Step 2. Exponents
• Simplify all expressions with exponents.
3. Step 3. Multiplication and Division
• Perform all multiplication and division in order from left to right. These operations have equal priority.
4. Step 4. Addition and Subtraction
• Perform all addition and subtraction in order from left to right. These operations have equal priority.

### Example 1

Simplify: $5+23+3[6−3(4−2)].5+23+3[6−3(4−2)].$

##### Practice Makes Perfect
1.

$3(1+9∙6)-423(1+9∙6)-42$

2.

$23-12÷(9-5)23-12÷(9-5)$

3.

$33÷3+4(7-2)33÷3+4(7-2)$

4.

$10+3[6-2(4-2)]-2410+3[6-2(4-2)]-24$

Evaluate the following expressions being sure to follow the order of operations:

5.

When $x=3x=3$ ,

1. $x5x5$
2. $5x5x$
3. $3x2-4x-83x2-4x-8$
6.

When $x=3,y=-2x=3,y=-2$
$6x2+3xy-9y26x2+3xy-9y2$

7.

When $x=-8,y=3x=-8,y=3$
$(x+y)2(x+y)2$

Simplify by combining like terms:

8.

$10a+7+5a-2+7a-410a+7+5a-2+7a-4$

9.

$5b+9b+10(2b+3b)+55b+9b+10(2b+3b)+5$

### How To

#### Solve linear equations using a general strategy

1. Step 1. Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.
2. Step 2. Collect all the variable terms on one side of the equation. Use the Addition or Subtraction Property of Equality.
3. Step 3. Collect all the constant terms on the other side of the equation. Use the Addition or Subtraction Property of Equality.
4. Step 4. Make the coefficient of the variable term equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation.
5. Step 5. Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.

### Example 2

Solve linear equations using a general strategy.

Solve for w

$2(w+5)+1=10+4w+22(w+5)+1=10+4w+2$

##### Practice Makes Perfect

Solve each linear equation using the general strategy.

10.

$15(y-9)=-6015(y-9)=-60$

11.

$-2(11-7x)+54=4-2(11-7x)+54=4$

12.

$3(4n-1)-2=8n+33(4n-1)-2=8n+3$

13.

$12+2(5-3y)=-9(y-1)-212+2(5-3y)=-9(y-1)-2$

14.

$14(20x+12)=x+714(20x+12)=x+7$

15.

$22(3m-4)=8(2m+9)22(3m-4)=8(2m+9)$

16.

$3x+42+1=5x+1083x+42+1=5x+108$

17.

$0.05n+0.10(n+8)=2.150.05n+0.10(n+8)=2.15$