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Simplifying -13(y + 3) + 5(4y + -7) = 6(y + -3) + 10 Reorder the terms: -13(3 + y) + 5(4y + -7) = 6(y + -3) + 10 (3 * -13 + y * -13) + 5(4y + -7) = 6(y + -3) + 10 (-39 + -13y) + 5(4y + -7) = 6(y + -3) + 10 Reorder the terms: -39 + -13y + 5(-7 + 4y) = 6(y + -3) + 10 -39 + -13y + (-7 * 5 + 4y * 5) = 6(y + -3) + 10 -39 + -13y + (-35 + 20y) = 6(y + -3) + 10 Reorder the terms: -39 + -35 + -13y + 20y = 6(y + -3) + 10 Combine like terms: -39 + -35 = -74 -74 + -13y + 20y = 6(y + -3) + 10 Combine like terms: -13y + 20y = 7y -74 + 7y = 6(y + -3) + 10 Reorder the terms: -74 + 7y = 6(-3 + y) + 10 -74 + 7y = (-3 * 6 + y * 6) + 10 -74 + 7y = (-18 + 6y) + 10 Reorder the terms: -74 + 7y = -18 + 10 + 6y Combine like terms: -18 + 10 = -8 -74 + 7y = -8 + 6y Solving -74 + 7y = -8 + 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. -74 + 7y + -6y = -8 + 6y + -6y Combine like terms: 7y + -6y = 1y -74 + 1y = -8 + 6y + -6y Combine like terms: 6y + -6y = 0 -74 + 1y = -8 + 0 -74 + 1y = -8 Add '74' to each side of the equation. -74 + 74 + 1y = -8 + 74 Combine like terms: -74 + 74 = 0 0 + 1y = -8 + 74 1y = -8 + 74 Combine like terms: -8 + 74 = 66 1y = 66 Divide each side by '1'. y = 66 Simplifying y = 66
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