1. 3.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Two-Step Equations

2. 3.2 Warm-Up Solve the equation. 1.3x = –18 ANSWER –6 ANSWER –10 2. b + 21 = 11 3. Simplify the expression 3 ( x + 2 ) – 4x + 1. ANSWER –x + 7

3. 3.2 Warm-Up 4.There are three times as many goats as sheep in a petting zoo. Find the number of sheep if the total number of goats and sheep is 28. ANSWER 7 sheep

4. 3.2 Example 1Solve + 5 = 11. x 2 Write original equation. + 5 = x 2 11 + 5 – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify. 2 = x 2 2 6 Multiply each side by 2. x = 12 Simplify. ANSWER The solution is 12. Check by substituting 12 for x in the original equation.

5. 3.2 Example 1 CHECK + 5 = x 2 11 Write original equation. 11 + 5 = 12 2 ? Substitute 12 for x. Simplify. Solution checks. 11 = 11

6. 3.2 Guided Practice Solve the equation. Check your solution. 1. 5x + 9 = 24 3 ANSWER 2. 4y – 4 = 16 5 ANSWER 3. –1 = – 7 z 3 18 ANSWER

7. 3.2 Example 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide each side by 3. x = 7 Simplify. = 3 3x3x 3 21

8. 3.2 Guided Practice 4. 4w + 2w = 24 Solve the equation. Check your solution. 4 ANSWER 5. 8t – 3t = 35 7 ANSWER 6. –16 = 5d – 9d 4 ANSWER

9. 3.2 Example 3 The output of a function is 3 less than 5 times the input. Find the input when the output is 17. y = 5x – 3 y is 3 less than 5 times x. SOLUTION Write an equation for the function. Let x be the input and y be the output STEP 1

10. 3.2 Example 3 Solve the equation for x when y = 17. STEP 2 y = 5x – 3 Write original function. 17 = 5x – 3 Substitute 17 for y. 17 + 3 = 5x – 3 + 3 Add 3 to each side. 20 = 5x Simplify. Divide each side by 5. 4 = x Simplify. ANSWER An input of 4 produces an output of 17. = 5 20 5x5x 5

11. 3.2 Example 3 Write original function. Substitute 17 for y and 4 for x. Multiply 5 and 4. Simplify. Solution checks. CHECK 17 = 20 – 3 ? 17 = 5(4) – 3 ? 17 = 17 y = 5x – 3

12. 3.2 Guided Practice 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. ANSWER –3 8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3 ANSWER 3 4 1

13. 3.2 Example 4 As a scuba diver descends into deeper water, the pressure of the water on the diver’s body steadily increases. SCUBA DIVING The pressure at the surface of the water is 2117 pounds per square foot ( lb/ft 2 ). The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the depth at which a diver experiences a pressure of 8517 pounds per square foot.

14. 3.2 Example 4 SOLUTION Write a verbal model. Then write an equation. STEP 1

15. 3.2 Example 4 Find the depth at which the pressure is 8517 pounds per square foot. P = 2117 + 64d Write equation. STEP 2 Substitute 8517 for P. 8517 – 2117 = 2117 – 2117 + 64d Subtract 2117 from each side. 8517 = 2117 + 64d 6400 = 64d Simplify. Divide each side by 64. 100 = d Simplify. ANSWER A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet. 64 6400 64 = 64d

16. 3.2 Example 4 P = 2117 + 64d Write original equation. Substitute 8517 for P and 100 for d. Multiply 64 and 100. Simplify. Solution checks. 8517 2117 + 6400 ? = 8517 2117 + 64(100) ? = CHECK 8517 = 8517

17. 3.2 Guided Practice WHAT IF? In Example 4, suppose the diver experiences a pressure of 5317 pounds per square foot. Find the diver’s depth. 9. ANSWER 50 ft Jobs Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work? 10. 5 h ANSWER

18. 3.2 Lesson Quiz Solve the equation. 1. + 6 = –14 a 4 ANSWER 80– 2. 6r – 12 = 6 ANSWER 3 3. 36 = 7y 2y + – ANSWER 4–

19. 3.2 Lesson Quiz The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is – 6. 4. ANSWER y = 3x 9; 1 – A bank charges $5.00 per month plus $0.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month. 5. ANSWER 11 checks