1. Solve an equation by combining like terms EXAMPLE 1 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – 10 + 10 = 20 + 10 Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify. = 30 5 5x5x 5 Solve

2. EXAMPLE 2 Solve an equation using the distributive property 7x + 2(x + 6) = 39. SOLUTION When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally. Solve

3. EXAMPLE 2 METHOD 1 Show All Steps 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 – 12 = 39 – 12 9x = 27 x = 3 = 9x9x 9 27 9 METHOD 2 Do Some Steps Mentally 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x = 27 x = 3

4. Standardized Test Practice EXAMPLE 3 SOLUTION ANSWER The correct answer is D. A CD B In Step 2, the distributive property is used to simplify the left side of the equation. Because – 4( x – 3) = – 4 x+ 12, Step 2 should be 5x – 4x + 12 = 17.

5. Write original equation. 7d + 4 = 32 Combine like terms. 7d + 4 – 4 = 32 – 4 Subtract 4 from each side. 7d = 28 Simplify Divide each side by 5. d = 4 Simplify. = 28 7 7d7d 7 GUIDED PRACTICE for Examples 1, 2, and 3 9d – 2d + 4 = 32 1. 9d – 2d + 4 = 32 Solve the equation. Check your solution.

6. Check GUIDED PRACTICE for Examples 1, 2, and 3 9d – 2d + 4 = 32 Write original equation. Substitute 4 for d. Multiply. 32 = 32 Simplify. Solution checks. 9(4) – 2(4) + 4 = 32 ? 36 – 8 + 4 = 32 ?

7. EXAMPLE 2 2w + 3w + 12 = 27 5w + 12 = 27 5w + 12 – 12 = 27 – 12 5w = 15 w = 3 = 5w5w 5 15 5 GUIDED PRACTICE for Examples 1, 2, and 3 2w + 3(w + 4) = 27 2. 2w + 3(w + 4) = 27 Solve the equation. Check your solution.

8. Check GUIDED PRACTICE for Examples 1, 2, and 3 Write original equation. Substitute 3 for w. Multiply. Simplify solution checks. 2w + 3(w +4) = 27 27 = 27 Simplify. 2(3) + 3(3 + 4) = 27 ? 6 + 21 = 27 ? 6 + 3(7) = 27 ?

9. EXAMPLE 2 6x – 2x + 10 = 46 4x + 10 = 46 4x + 10 – 10 = 46 – 10 4x = 36 x = 9 = 4x4x 4 36 4 GUIDED PRACTICE for Examples 1, 2, and 3 6x – 2(x – 5) = 46 3. Solve the equation. Check your solution. 6x – 2(x – 5) = 46

10. Check GUIDED PRACTICE for Examples1, 2, and 3 6x – 2(x – 5) = 46 46 = 46 6(9) – 2(9 – 5) = 46 ? 54 – 8 = 46 ? 54 – 2(4) = 46 ?