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Simplifying 0.5(y + 8) + 5 = 0.25(8y + -14) + -7 Reorder the terms: 0.5(8 + y) + 5 = 0.25(8y + -14) + -7 (8 * 0.5 + y * 0.5) + 5 = 0.25(8y + -14) + -7 (4 + 0.5y) + 5 = 0.25(8y + -14) + -7 Reorder the terms: 4 + 5 + 0.5y = 0.25(8y + -14) + -7 Combine like terms: 4 + 5 = 9 9 + 0.5y = 0.25(8y + -14) + -7 Reorder the terms: 9 + 0.5y = 0.25(-14 + 8y) + -7 9 + 0.5y = (-14 * 0.25 + 8y * 0.25) + -7 9 + 0.5y = (-3.5 + 2y) + -7 Reorder the terms: 9 + 0.5y = -3.5 + -7 + 2y Combine like terms: -3.5 + -7 = -10.5 9 + 0.5y = -10.5 + 2y Solving 9 + 0.5y = -10.5 + 2y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2y' to each side of the equation. 9 + 0.5y + -2y = -10.5 + 2y + -2y Combine like terms: 0.5y + -2y = -1.5y 9 + -1.5y = -10.5 + 2y + -2y Combine like terms: 2y + -2y = 0 9 + -1.5y = -10.5 + 0 9 + -1.5y = -10.5 Add '-9' to each side of the equation. 9 + -9 + -1.5y = -10.5 + -9 Combine like terms: 9 + -9 = 0 0 + -1.5y = -10.5 + -9 -1.5y = -10.5 + -9 Combine like terms: -10.5 + -9 = -19.5 -1.5y = -19.5 Divide each side by '-1.5'. y = 13 Simplifying y = 13
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