EXAMPLE 1 Solve an equation with a variable on one side

Solve 45

x + 8 = 20.

45

x + 8 = 20

45

x = 12

x = (12)54

x = 15

Write original equation.

Subtract 8 from each side.

Multiply each side by , the reciprocal of .

544

5Simplify.

ANSWER The solution is 15.

CHECK x = 15 in the original equation.

45

45

x + 8 = (15) + 8 = 12 + 8 = 20

EXAMPLE 2 Write and use a linear equation

During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills?

Restaurant

SOLUTION

Write a verbal model. Then write an equation. Write 15% as a decimal.

EXAMPLE 2 Write and use a linear equation

105 = 30 + 0.15x

75 = 0.15x

500 = x

Write equation.

Subtract 30 from each side.

Divide each side by 0.15.

The total of the customers’ food bills is $500.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

Solve the equation. Check your solution.

1. 4x + 9 = 21

SOLUTION

4x + 9 = 21 Write original equation.

Subtract 9 from each side.

Divide each side by 4.

4x = 12

x = 3

ANSWER The solution is x = 3.

GUIDED PRACTICE for Examples 1 and 2

Check x = 3 in the original equation.

4(3) + 9 = 12 + 9

= 21

GUIDED PRACTICE for Examples 1 and 2

Solve the equation. Check your solution.

2. 7x – 41 = – 13

SOLUTION

7x – 41 = – 13 Write original equation.

Add 41 to each side.

Divide each side by 7.

7x = 28

x = 4

ANSWER The solution is x = 4.

GUIDED PRACTICE for Examples 1 and 2

Check x = 4 in the original equation.

7x – 41 = 7(4) – 41

= – 13

GUIDED PRACTICE for Examples 1 and 2

Solve the equation. Check your solution.

35

–3. x + 1 = 4

SOLUTION

Write original equation.

Simplify.

ANSWER The solution is 5.

35

– x + 1 = 4

x = – (3)53

x = – 5

Multiply each side by , the reciprocal of .

53

–35

–

Subtract 1 from each side.35

– x = 3

GUIDED PRACTICE for Examples 1 and 2

Check x = – 5 in the original equation.

= 4

35

– x + 1 = 35

– (– 5)+ 1

GUIDED PRACTICE for Examples 1 and 2

A real estate agent’s base salary is $22,000 per year. The agent earns a 4% commission on total sales. How much must the agent sell to earn $60,000 in one year?

4. REAL ESTATE

GUIDED PRACTICE for Examples 1 and 2

Write a verbal model. Then write an equation. Write 4% as a decimal.

Income

(dollars)

Salary

(dollars)commission

Sell

(dollars)

60000 22000 0.04 x

= +

+=

38000 = 0.04x

950000 = x

Subtract 22000 from each side.

Divide each side by 0.15.

The agent must sell $950,000 in a year to each $ 60000

ANSWER

SOLUTION