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Simplifying -52 + 21y + 6 = 6(4y + -3) + -7 Reorder the terms: -52 + 6 + 21y = 6(4y + -3) + -7 Combine like terms: -52 + 6 = -46 -46 + 21y = 6(4y + -3) + -7 Reorder the terms: -46 + 21y = 6(-3 + 4y) + -7 -46 + 21y = (-3 * 6 + 4y * 6) + -7 -46 + 21y = (-18 + 24y) + -7 Reorder the terms: -46 + 21y = -18 + -7 + 24y Combine like terms: -18 + -7 = -25 -46 + 21y = -25 + 24y Solving -46 + 21y = -25 + 24y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-24y' to each side of the equation. -46 + 21y + -24y = -25 + 24y + -24y Combine like terms: 21y + -24y = -3y -46 + -3y = -25 + 24y + -24y Combine like terms: 24y + -24y = 0 -46 + -3y = -25 + 0 -46 + -3y = -25 Add '46' to each side of the equation. -46 + 46 + -3y = -25 + 46 Combine like terms: -46 + 46 = 0 0 + -3y = -25 + 46 -3y = -25 + 46 Combine like terms: -25 + 46 = 21 -3y = 21 Divide each side by '-3'. y = -7 Simplifying y = -7
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