1. EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x 2 =

2. EXAMPLE 2 Solve a Multi-Step Problem Each side of the triangle has the same length. What is the perimeter of the triangle? SOLUTION 5x + 9 = 7x + 5 Write an equation. 5x + 9 –5x = 7x + 5 –5x Subtract 5x from each side. 9 = 2x + 5 Simplify. 9 –5 = 2x + 5–5 Subtract 5 from each side. 4 = 2x Simplify. 4 2 2x2x 2 = Divide each side by 2 2 = x Simplify.

3. EXAMPLE 2 Solve a Multi-Step Problem Because 5x + 9 = 5(2) + 9 = 19, each side of the triangle is 19 units long. Since each side of the triangle has the same length, the perimeter is 3 19, or 57 units. The perimeter of the triangle is 57 units. ANSWER

4. EXAMPLE 3 Using the Distributive Property 21x = 3(2x + 30) Original equation. 21x –6x = 6x + 90 –6x Subtract 6x from each side. 15x = 90 Simplify. Divide each side by 15 x = 6 Simplify. 21x = 6x + 90 Distributive property 15 15x 15 90 =

5. GUIDED PRACTICE for Examples 1, 2, and 3 55 + 3x = 8x 1. 11 = x Solve the equation.

6. GUIDED PRACTICE for Examples 1, 2, and 3 9x = 12x – 9 2. x = 3

7. GUIDED PRACTICE for Examples 1, 2, and 3 –15x + 120 = 15x 3. 4 = x

8. GUIDED PRACTICE for Examples 1, 2, and 3 4. 4a + 5 = a + 11 2 = a

9. GUIDED PRACTICE for Examples 1, 2, and 3 n = –8 3n + 7 = 2n –1 5.

10. GUIDED PRACTICE for Examples 1, 2, and 3 –6c + 1 = –9c + 7 6. c = 2

11. GUIDED PRACTICE for Examples 1, 2, and 3 5 = s 28 –3s = 5s –12 7.

12. GUIDED PRACTICE for Examples 1, 2, and 3 w = –18 4(w – 9) = 7w + 18 8.

13. GUIDED PRACTICE for Examples 1, 2, and 3 y = –3 9. 2(y + 4) = –3y – 7