Chapter 6 - Section 6.3 - Equations with Parentheses - Exercises - Page 242: 53

y=-2

Simplifying 6(y + -4) + -4(5y + 1) = 3(y + -2) + -4(2y + 1) Reorder the terms: 6(-4 + y) + -4(5y + 1) = 3(y + -2) + -4(2y + 1) (-4 * 6 + y * 6) + -4(5y + 1) = 3(y + -2) + -4(2y + 1) (-24 + 6y) + -4(5y + 1) = 3(y + -2) + -4(2y + 1) Reorder the terms: -24 + 6y + -4(1 + 5y) = 3(y + -2) + -4(2y + 1) -24 + 6y + (1 * -4 + 5y * -4) = 3(y + -2) + -4(2y + 1) -24 + 6y + (-4 + -20y) = 3(y + -2) + -4(2y + 1) Reorder the terms: -24 + -4 + 6y + -20y = 3(y + -2) + -4(2y + 1) Combine like terms: -24 + -4 = -28 -28 + 6y + -20y = 3(y + -2) + -4(2y + 1) Combine like terms: 6y + -20y = -14y -28 + -14y = 3(y + -2) + -4(2y + 1) Reorder the terms: -28 + -14y = 3(-2 + y) + -4(2y + 1) -28 + -14y = (-2 * 3 + y * 3) + -4(2y + 1) -28 + -14y = (-6 + 3y) + -4(2y + 1) Reorder the terms: -28 + -14y = -6 + 3y + -4(1 + 2y) -28 + -14y = -6 + 3y + (1 * -4 + 2y * -4) -28 + -14y = -6 + 3y + (-4 + -8y) Reorder the terms: -28 + -14y = -6 + -4 + 3y + -8y Combine like terms: -6 + -4 = -10 -28 + -14y = -10 + 3y + -8y Combine like terms: 3y + -8y = -5y -28 + -14y = -10 + -5y Solving -28 + -14y = -10 + -5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5y' to each side of the equation. -28 + -14y + 5y = -10 + -5y + 5y Combine like terms: -14y + 5y = -9y -28 + -9y = -10 + -5y + 5y Combine like terms: -5y + 5y = 0 -28 + -9y = -10 + 0 -28 + -9y = -10 Add '28' to each side of the equation. -28 + 28 + -9y = -10 + 28 Combine like terms: -28 + 28 = 0 0 + -9y = -10 + 28 -9y = -10 + 28 Combine like terms: -10 + 28 = 18 -9y = 18 Divide each side by '-9'. y = -2 Simplifying y = -2