Chapter 6 - Section 6.3 - Equations with Parentheses - Exercises - Page 242: 42

y=0.5

Simplifying 2(7y + -6) + -11(y + 1) = 38 + -7(9y + 4) Reorder the terms: 2(-6 + 7y) + -11(y + 1) = 38 + -7(9y + 4) (-6 * 2 + 7y * 2) + -11(y + 1) = 38 + -7(9y + 4) (-12 + 14y) + -11(y + 1) = 38 + -7(9y + 4) Reorder the terms: -12 + 14y + -11(1 + y) = 38 + -7(9y + 4) -12 + 14y + (1 * -11 + y * -11) = 38 + -7(9y + 4) -12 + 14y + (-11 + -11y) = 38 + -7(9y + 4) Reorder the terms: -12 + -11 + 14y + -11y = 38 + -7(9y + 4) Combine like terms: -12 + -11 = -23 -23 + 14y + -11y = 38 + -7(9y + 4) Combine like terms: 14y + -11y = 3y -23 + 3y = 38 + -7(9y + 4) Reorder the terms: -23 + 3y = 38 + -7(4 + 9y) -23 + 3y = 38 + (4 * -7 + 9y * -7) -23 + 3y = 38 + (-28 + -63y) Combine like terms: 38 + -28 = 10 -23 + 3y = 10 + -63y Solving -23 + 3y = 10 + -63y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '63y' to each side of the equation. -23 + 3y + 63y = 10 + -63y + 63y Combine like terms: 3y + 63y = 66y -23 + 66y = 10 + -63y + 63y Combine like terms: -63y + 63y = 0 -23 + 66y = 10 + 0 -23 + 66y = 10 Add '23' to each side of the equation. -23 + 23 + 66y = 10 + 23 Combine like terms: -23 + 23 = 0 0 + 66y = 10 + 23 66y = 10 + 23 Combine like terms: 10 + 23 = 33 66y = 33 Divide each side by '66'. y = 0.5 Simplifying y = 0.5