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Simplifying -11(y + 1) + 5(3y + -7) = 3(y + -5) + 12 Reorder the terms: -11(1 + y) + 5(3y + -7) = 3(y + -5) + 12 (1 * -11 + y * -11) + 5(3y + -7) = 3(y + -5) + 12 (-11 + -11y) + 5(3y + -7) = 3(y + -5) + 12 Reorder the terms: -11 + -11y + 5(-7 + 3y) = 3(y + -5) + 12 -11 + -11y + (-7 * 5 + 3y * 5) = 3(y + -5) + 12 -11 + -11y + (-35 + 15y) = 3(y + -5) + 12 Reorder the terms: -11 + -35 + -11y + 15y = 3(y + -5) + 12 Combine like terms: -11 + -35 = -46 -46 + -11y + 15y = 3(y + -5) + 12 Combine like terms: -11y + 15y = 4y -46 + 4y = 3(y + -5) + 12 Reorder the terms: -46 + 4y = 3(-5 + y) + 12 -46 + 4y = (-5 * 3 + y * 3) + 12 -46 + 4y = (-15 + 3y) + 12 Reorder the terms: -46 + 4y = -15 + 12 + 3y Combine like terms: -15 + 12 = -3 -46 + 4y = -3 + 3y Solving -46 + 4y = -3 + 3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3y' to each side of the equation. -46 + 4y + -3y = -3 + 3y + -3y Combine like terms: 4y + -3y = 1y -46 + 1y = -3 + 3y + -3y Combine like terms: 3y + -3y = 0 -46 + 1y = -3 + 0 -46 + 1y = -3 Add '46' to each side of the equation. -46 + 46 + 1y = -3 + 46 Combine like terms: -46 + 46 = 0 0 + 1y = -3 + 46 1y = -3 + 46 Combine like terms: -3 + 46 = 43 1y = 43 Divide each side by '1'. y = 43 Simplifying y = 43
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