1. Solve an equation with a variable on one side
EXAMPLE 1
Solve an equation with a variable on one side
Solve 4 5
x + 8 = 20. 4 5
x + 8 = 20
Write original equation. 4 5
x = 12
Subtract 8 from each side.
x = (12) 5 4
Multiply each side by , the reciprocal of 5 4
x = 15
Simplify.
ANSWER
The solution is 15.
CHECK
x = 15 in the original equation. 4 5
x + 8 =
(15) + 8 = = 20

2. 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.

3. Write and use a linear equation
EXAMPLE 2
Write and use a linear equation
105 = x
Write equation.
75 = 0.15x
Subtract 30 from each side.
500 = x
Divide each side by 0.15.
The total of the customers’ food bills is $500.
ANSWER

4. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
x + 9 = 21
SOLUTION
4x + 9 = 21
Write original equation.
4x = 12
Subtract 9 from each side.
x = 3
Divide each side by 4.
ANSWER
The solution is x = 3.

5. GUIDED PRACTICE
for Examples 1 and 2
Check x = 3 in the original equation.
4(3) + 9 =
= 21 

6. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
x – 41 = – 13
SOLUTION
7x – 41 = – 13
Write original equation.
7x = 28
Add 41 to each side.
x = 4
Divide each side by 7.
ANSWER
The solution is x = 4.

7. GUIDED PRACTICE
for Examples 1 and 2
Check x = 4 in the original equation.
7x – 41 = 7(4) – 41
= – 13 

8. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution. 3 5 – 3.
x + 1 = 4
SOLUTION 3 5 –
x + 1 = 4
Write original equation. 3 5 –
x = 3
Subtract 1 from each side.
x = – (3) 5 3
Multiply each side by , the reciprocal of 5 3 –
x = – 5
Simplify.
ANSWER
The solution is 5.

9. GUIDED PRACTICE
for Examples 1 and 2
Check x = – 5 in the original equation. 3 5 –
x + 1 =
(– 5)+ 1
= 4 

10. GUIDED PRACTICE
for Examples 1 and 2 4.
REAL ESTATE
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?

11. Write a verbal model. Then write an equation. Write 4% as a decimal.
GUIDED PRACTICE
for Examples 1 and 2
SOLUTION
Write a verbal model. Then write an equation. Write 4% as a decimal.
Income
(dollars)
Salary
commission
Sell
60000
22000
0.04 x = +
38000 = 0.04x
Subtract from each side.
= x
Divide each side by 0.15.
The agent must sell $950,000 in a year to each $ 60000
ANSWER