1. EXAMPLE 1 Solve an equation with a variable on one side Solve 4 5 x + 8 = 20. 4 5 x + 8 = 20 4 5 x = 12 x = (12) 5 4 x = 15 Write original equation. Subtract 8 from each side. Multiply each side by, the reciprocal of. 5 44 5 Simplify. ANSWER The solution is 15. CHECK x = 15 in the original equation. 4 5 4 5 x + 8 = (15) + 8 = 12 + 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. 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

4. GUIDED PRACTICE for Examples 1 and 2 Solve the equation. Check your solution. 1. 4x + 9 = 21 ANSWER The solution is x = 3. 2. 7x – 41 = – 13 ANSWER The solution is x = 4. ANSWER The solution is 5. 3. 3 5 – x + 1 = 4

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