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Simplifying -17(y + 1) + 6(4y + -6) = 6(y + -5) + 9 Reorder the terms: -17(1 + y) + 6(4y + -6) = 6(y + -5) + 9 (1 * -17 + y * -17) + 6(4y + -6) = 6(y + -5) + 9 (-17 + -17y) + 6(4y + -6) = 6(y + -5) + 9 Reorder the terms: -17 + -17y + 6(-6 + 4y) = 6(y + -5) + 9 -17 + -17y + (-6 * 6 + 4y * 6) = 6(y + -5) + 9 -17 + -17y + (-36 + 24y) = 6(y + -5) + 9 Reorder the terms: -17 + -36 + -17y + 24y = 6(y + -5) + 9 Combine like terms: -17 + -36 = -53 -53 + -17y + 24y = 6(y + -5) + 9 Combine like terms: -17y + 24y = 7y -53 + 7y = 6(y + -5) + 9 Reorder the terms: -53 + 7y = 6(-5 + y) + 9 -53 + 7y = (-5 * 6 + y * 6) + 9 -53 + 7y = (-30 + 6y) + 9 Reorder the terms: -53 + 7y = -30 + 9 + 6y Combine like terms: -30 + 9 = -21 -53 + 7y = -21 + 6y Solving -53 + 7y = -21 + 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. -53 + 7y + -6y = -21 + 6y + -6y Combine like terms: 7y + -6y = 1y -53 + 1y = -21 + 6y + -6y Combine like terms: 6y + -6y = 0 -53 + 1y = -21 + 0 -53 + 1y = -21 Add '53' to each side of the equation. -53 + 53 + 1y = -21 + 53 Combine like terms: -53 + 53 = 0 0 + 1y = -21 + 53 1y = -21 + 53 Combine like terms: -21 + 53 = 32 1y = 32 Divide each side by '1'. y = 32 Simplifying y = 32
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