Solve an equation with a variable on one side

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Presentation transcript:

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 = 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.

Write and use a linear equation EXAMPLE 2 Write and use a linear equation 105 = 30 + 0.15x 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

Solve the equation. Check your solution. GUIDED PRACTICE for Examples 1 and 2 Solve the equation. Check your solution. 1. 4x + 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.

GUIDED PRACTICE for Examples 1 and 2 Check x = 3 in the original equation. 4(3) + 9 = 12 + 9 = 21 

Solve the equation. Check your solution. GUIDED PRACTICE for Examples 1 and 2 Solve the equation. Check your solution. 2. 7x – 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.

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

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.

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

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?

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 22000 from each side. 950000 = x Divide each side by 0.15. The agent must sell $950,000 in a year to each $ 60000 ANSWER