1. 2.3 Solve two-step equations You will solve two-step equations Essential question: How do you solve two-step equations?

2. Warm-Up Exercises EXAMPLE 1 Solve a two-step equation Solve + 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.

3. Warm-Up Exercises EXAMPLE 1 Solve a two-step equation CHECK + 5 = x 2 11 Write original equation. 11 + 5 = 12 2 ? Substitute 12 for x. Simplify. Solution checks. 11 = 11

4. Warm-Up Exercises GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 1. 5x + 9 = 24 3 ANSWER

5. Warm-Up Exercises GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 2. 4y – 4 = 16 5 ANSWER

6. Warm-Up Exercises GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 3. –1 = – 7 z 3 18 ANSWER

7. Warm-Up Exercises Solve a two-step equation by combining like terms 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. Warm-Up Exercises Find an input of a function 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 Solve the equation for x when y = 17. STEP 2

9. Warm-Up Exercises Find an input of a function EXAMPLE 3 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

10. Warm-Up Exercises Find an input of a function 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

11. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 4. 4w + 2w = 24 Solve the equation. Check your solution. 4 ANSWER

12. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 5. 8t – 3t = 35 Solve the equation. Check your solution. 7 ANSWER

13. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 6. –16 = 5d – 9d Solve the equation. Check your solution. 4 ANSWER

14. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. ANSWER –3

15. Warm-Up Exercises GUIDED PRACTICE for Examples 2 And 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

16. Warm-Up Exercises EXAMPLE 4 Solve a multi-step problem 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.

17. Warm-Up Exercises SOLUTION EXAMPLE 1 Write a verbal model. Then write an equation. Find the depth at which the pressure is 8517 pounds per square foot. P = 2117 + 64d Write equation. STEP 1 STEP 2 EXAMPLE 4 Solve a multi-step problem

18. Warm-Up Exercises GUIDED PRACTICE 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 EXAMPLE 4 Solve a multi-step problem

19. Warm-Up Exercises GUIDED PRACTICE 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 EXAMPLE 4 Solve a multi-step problem 8517 = 8517

20. Warm-Up Exercises GUIDED PRACTICE for Example 4 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

21. Warm-Up Exercises GUIDED PRACTICE for Example 4 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

22. Warm-Up Exercises Daily Homework Quiz Solve the equation. 1. + 6 = –14 a 4 ANSWER 80– 2. 6r – 12 = 6 ANSWER 3 3. 36 = 7y 2y + – ANSWER 4–

23. Warm-Up Exercises Daily Homework 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 $.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

24. You will solve two-step equations Essential question: How do you solve two-step equations? First look for like terms and combine them when solving two-step equations. For equations with tow operations, look at the original equation and apply the inverse operations in the reverse order. To solve equations efficiently, apply inverse operations in the reverse order of the operations performed on the variable. Combine like terms before solving equations.