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Simplifying -7(y + 3) + 3(4y + -6) = 4(y + -5) + 13 Reorder the terms: -7(3 + y) + 3(4y + -6) = 4(y + -5) + 13 (3 * -7 + y * -7) + 3(4y + -6) = 4(y + -5) + 13 (-21 + -7y) + 3(4y + -6) = 4(y + -5) + 13 Reorder the terms: -21 + -7y + 3(-6 + 4y) = 4(y + -5) + 13 -21 + -7y + (-6 * 3 + 4y * 3) = 4(y + -5) + 13 -21 + -7y + (-18 + 12y) = 4(y + -5) + 13 Reorder the terms: -21 + -18 + -7y + 12y = 4(y + -5) + 13 Combine like terms: -21 + -18 = -39 -39 + -7y + 12y = 4(y + -5) + 13 Combine like terms: -7y + 12y = 5y -39 + 5y = 4(y + -5) + 13 Reorder the terms: -39 + 5y = 4(-5 + y) + 13 -39 + 5y = (-5 * 4 + y * 4) + 13 -39 + 5y = (-20 + 4y) + 13 Reorder the terms: -39 + 5y = -20 + 13 + 4y Combine like terms: -20 + 13 = -7 -39 + 5y = -7 + 4y Solving -39 + 5y = -7 + 4y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4y' to each side of the equation. -39 + 5y + -4y = -7 + 4y + -4y Combine like terms: 5y + -4y = 1y -39 + 1y = -7 + 4y + -4y Combine like terms: 4y + -4y = 0 -39 + 1y = -7 + 0 -39 + 1y = -7 Add '39' to each side of the equation. -39 + 39 + 1y = -7 + 39 Combine like terms: -39 + 39 = 0 0 + 1y = -7 + 39 1y = -7 + 39 Combine like terms: -7 + 39 = 32 1y = 32 Divide each side by '1'. y = 32 Simplifying y = 32
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