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Simplifying -17(y + 2) + 6(4y + -3) = 6(y + -3) + 12 Reorder the terms: -17(2 + y) + 6(4y + -3) = 6(y + -3) + 12 (2 * -17 + y * -17) + 6(4y + -3) = 6(y + -3) + 12 (-34 + -17y) + 6(4y + -3) = 6(y + -3) + 12 Reorder the terms: -34 + -17y + 6(-3 + 4y) = 6(y + -3) + 12 -34 + -17y + (-3 * 6 + 4y * 6) = 6(y + -3) + 12 -34 + -17y + (-18 + 24y) = 6(y + -3) + 12 Reorder the terms: -34 + -18 + -17y + 24y = 6(y + -3) + 12 Combine like terms: -34 + -18 = -52 -52 + -17y + 24y = 6(y + -3) + 12 Combine like terms: -17y + 24y = 7y -52 + 7y = 6(y + -3) + 12 Reorder the terms: -52 + 7y = 6(-3 + y) + 12 -52 + 7y = (-3 * 6 + y * 6) + 12 -52 + 7y = (-18 + 6y) + 12 Reorder the terms: -52 + 7y = -18 + 12 + 6y Combine like terms: -18 + 12 = -6 -52 + 7y = -6 + 6y Solving -52 + 7y = -6 + 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. -52 + 7y + -6y = -6 + 6y + -6y Combine like terms: 7y + -6y = 1y -52 + 1y = -6 + 6y + -6y Combine like terms: 6y + -6y = 0 -52 + 1y = -6 + 0 -52 + 1y = -6 Add '52' to each side of the equation. -52 + 52 + 1y = -6 + 52 Combine like terms: -52 + 52 = 0 0 + 1y = -6 + 52 1y = -6 + 52 Combine like terms: -6 + 52 = 46 1y = 46 Divide each side by '1'. y = 46 Simplifying y = 46
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