Chapter 6 - Section 6.3 - Equations with Parentheses - Exercises - Page 242: 35

x=2

Simplifying 3(2x + 7) = 13 + 2(4x + 2) Reorder the terms: 3(7 + 2x) = 13 + 2(4x + 2) (7 * 3 + 2x * 3) = 13 + 2(4x + 2) (21 + 6x) = 13 + 2(4x + 2) Reorder the terms: 21 + 6x = 13 + 2(2 + 4x) 21 + 6x = 13 + (2 * 2 + 4x * 2) 21 + 6x = 13 + (4 + 8x) Combine like terms: 13 + 4 = 17 21 + 6x = 17 + 8x Solving 21 + 6x = 17 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 21 + 6x + -8x = 17 + 8x + -8x Combine like terms: 6x + -8x = -2x 21 + -2x = 17 + 8x + -8x Combine like terms: 8x + -8x = 0 21 + -2x = 17 + 0 21 + -2x = 17 Add '-21' to each side of the equation. 21 + -21 + -2x = 17 + -21 Combine like terms: 21 + -21 = 0 0 + -2x = 17 + -21 -2x = 17 + -21 Combine like terms: 17 + -21 = -4 -2x = -4 Divide each side by '-2'. x = 2 Simplifying x = 2