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Simplifying -5(y + 3) + 4(3y + -3) = 6(y + -5) + 13 Reorder the terms: -5(3 + y) + 4(3y + -3) = 6(y + -5) + 13 (3 * -5 + y * -5) + 4(3y + -3) = 6(y + -5) + 13 (-15 + -5y) + 4(3y + -3) = 6(y + -5) + 13 Reorder the terms: -15 + -5y + 4(-3 + 3y) = 6(y + -5) + 13 -15 + -5y + (-3 * 4 + 3y * 4) = 6(y + -5) + 13 -15 + -5y + (-12 + 12y) = 6(y + -5) + 13 Reorder the terms: -15 + -12 + -5y + 12y = 6(y + -5) + 13 Combine like terms: -15 + -12 = -27 -27 + -5y + 12y = 6(y + -5) + 13 Combine like terms: -5y + 12y = 7y -27 + 7y = 6(y + -5) + 13 Reorder the terms: -27 + 7y = 6(-5 + y) + 13 -27 + 7y = (-5 * 6 + y * 6) + 13 -27 + 7y = (-30 + 6y) + 13 Reorder the terms: -27 + 7y = -30 + 13 + 6y Combine like terms: -30 + 13 = -17 -27 + 7y = -17 + 6y Solving -27 + 7y = -17 + 6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6y' to each side of the equation. -27 + 7y + -6y = -17 + 6y + -6y Combine like terms: 7y + -6y = 1y -27 + 1y = -17 + 6y + -6y Combine like terms: 6y + -6y = 0 -27 + 1y = -17 + 0 -27 + 1y = -17 Add '27' to each side of the equation. -27 + 27 + 1y = -17 + 27 Combine like terms: -27 + 27 = 0 0 + 1y = -17 + 27 1y = -17 + 27 Combine like terms: -17 + 27 = 10 1y = 10 Divide each side by '1'. y = 10 Simplifying y = 10
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