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Simplifying -8(y + 3) + 3(4y + -7) = 3(y + -4) + 13 Reorder the terms: -8(3 + y) + 3(4y + -7) = 3(y + -4) + 13 (3 * -8 + y * -8) + 3(4y + -7) = 3(y + -4) + 13 (-24 + -8y) + 3(4y + -7) = 3(y + -4) + 13 Reorder the terms: -24 + -8y + 3(-7 + 4y) = 3(y + -4) + 13 -24 + -8y + (-7 * 3 + 4y * 3) = 3(y + -4) + 13 -24 + -8y + (-21 + 12y) = 3(y + -4) + 13 Reorder the terms: -24 + -21 + -8y + 12y = 3(y + -4) + 13 Combine like terms: -24 + -21 = -45 -45 + -8y + 12y = 3(y + -4) + 13 Combine like terms: -8y + 12y = 4y -45 + 4y = 3(y + -4) + 13 Reorder the terms: -45 + 4y = 3(-4 + y) + 13 -45 + 4y = (-4 * 3 + y * 3) + 13 -45 + 4y = (-12 + 3y) + 13 Reorder the terms: -45 + 4y = -12 + 13 + 3y Combine like terms: -12 + 13 = 1 -45 + 4y = 1 + 3y Solving -45 + 4y = 1 + 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. -45 + 4y + -3y = 1 + 3y + -3y Combine like terms: 4y + -3y = 1y -45 + 1y = 1 + 3y + -3y Combine like terms: 3y + -3y = 0 -45 + 1y = 1 + 0 -45 + 1y = 1 Add '45' to each side of the equation. -45 + 45 + 1y = 1 + 45 Combine like terms: -45 + 45 = 0 0 + 1y = 1 + 45 1y = 1 + 45 Combine like terms: 1 + 45 = 46 1y = 46 Divide each side by '1'. y = 46 Simplifying y = 46
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