1. 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

2. 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. SOLUTION y = 5x – 3 y is 3 less than 5 times x. 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

3. 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 5 5x5x

4. 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 y = 5x – 3 17 = 20 – 3 ? 17 = 5(4) – 3 ? 17 = 17

5. GUIDED PRACTICE for Examples 2 and 3 4. 4w + 2w = 24 4w + 2w = 24 Write original equation. 6w = 24 Combine like terms. Divide each side by 6 w = 4 Simplify. 6 = 6w 6 21 Solve the equation. Check your solution.

6. GUIDED PRACTICE for Examples 2 and 3 Write original function. Multiply Simplify. Solution checks. CHECK 4w + 2w = 3 16 + 20 = 3 ? 4(4) + 2(4) = 24 ? Substitute 4 for w. 24 = 24

7. GUIDED PRACTICE for Examples 2 and 3 8t – 3t = 35 Write original equation. 5t = 35 Substract the like terms Divide each side by 5 t = 7 Simplify. 5 = 5t5t 5 35 5. 8t – 3t = 35 Solve the equation. Check your solution.

8. GUIDED PRACTICE for Examples 2 and 3 CHECK 8t – 3t = 35 Write original equation. Multiply. 35 =35 8(7) – 3(7) = 35 ? Substitute 7 for t. 56 – 21 = 35 ? Simplify. Solution checks.

9. GUIDED PRACTICE for Examples 2 and 3 6. –16 = 5d – 9d –16 = 5d – 9d Write original equation. –16 = – 4d Divide each side by –4 4 = d Simplify. – 4 = – 16 – 4 – 4d Substract the like terms Solve the equation. Check your solution.

10. GUIDED PRACTICE for Examples 2 and 3 Write original equation. Substitute 4 for d. Multiply Simplify. Solution checks. CHECK –16 = 5d –9d –16 = 20 – 36 ? –16 = 5(4) – 9(4) ? –16 = –16

11. GUIDED PRACTICE for Examples 2 and 3 y = – 2x + 5 y is 5 more than – 2 times x. 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 = 11. STEP 2 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. SOLUTION

12. GUIDED PRACTICE for Examples 2 and 3 y = 2x + 5 Write original function. 11 = – 2x + 5 Substitute 11 for y. 11 – 5 = – 2x + 5– 5 6 = – 2x Simplify. Divide each side by – 2. – 3 = x Simplify. ANSWER An input of – 3 produces an output of 11. = – 2 6 2x2x Substract 5 from each side

13. GUIDED PRACTICE for Examples 2 And 3 y = 4x – 4 y is 4 less than 4 times x. 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 = 3. STEP 2 8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3 SOLUTION

14. GUIDED PRACTICE for Examples 2 And 3 y = 4x – 4 Write original function. 3 = 4x – 4 Substitute 3 for y. 3 +4 = 4x – 4 + 4 Add 4 to each side. 7 = 4x Simplify. Divide each side by 4. Simplify. = 4 7 4 4x4x 3 4 1 = x ANSWER An input of produces an output of 3. 3 4 1