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Simplifying -9(y + 3) + 5(3y + -7) = 5(y + -4) + 10 Reorder the terms: -9(3 + y) + 5(3y + -7) = 5(y + -4) + 10 (3 * -9 + y * -9) + 5(3y + -7) = 5(y + -4) + 10 (-27 + -9y) + 5(3y + -7) = 5(y + -4) + 10 Reorder the terms: -27 + -9y + 5(-7 + 3y) = 5(y + -4) + 10 -27 + -9y + (-7 * 5 + 3y * 5) = 5(y + -4) + 10 -27 + -9y + (-35 + 15y) = 5(y + -4) + 10 Reorder the terms: -27 + -35 + -9y + 15y = 5(y + -4) + 10 Combine like terms: -27 + -35 = -62 -62 + -9y + 15y = 5(y + -4) + 10 Combine like terms: -9y + 15y = 6y -62 + 6y = 5(y + -4) + 10 Reorder the terms: -62 + 6y = 5(-4 + y) + 10 -62 + 6y = (-4 * 5 + y * 5) + 10 -62 + 6y = (-20 + 5y) + 10 Reorder the terms: -62 + 6y = -20 + 10 + 5y Combine like terms: -20 + 10 = -10 -62 + 6y = -10 + 5y Solving -62 + 6y = -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. -62 + 6y + -5y = -10 + 5y + -5y Combine like terms: 6y + -5y = 1y -62 + 1y = -10 + 5y + -5y Combine like terms: 5y + -5y = 0 -62 + 1y = -10 + 0 -62 + 1y = -10 Add '62' to each side of the equation. -62 + 62 + 1y = -10 + 62 Combine like terms: -62 + 62 = 0 0 + 1y = -10 + 62 1y = -10 + 62 Combine like terms: -10 + 62 = 52 1y = 52 Divide each side by '1'. y = 52 Simplifying y = 52
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