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Simplifying 0.5(x + 8) + 5 = 0.25(8x + 14) + -7 Reorder the terms: 0.5(8 + x) + 5 = 0.25(8x + 14) + -7 (8 * 0.5 + x * 0.5) + 5 = 0.25(8x + 14) + -7 (4 + 0.5x) + 5 = 0.25(8x + 14) + -7 Reorder the terms: 4 + 5 + 0.5x = 0.25(8x + 14) + -7 Combine like terms: 4 + 5 = 9 9 + 0.5x = 0.25(8x + 14) + -7 Reorder the terms: 9 + 0.5x = 0.25(14 + 8x) + -7 9 + 0.5x = (14 * 0.25 + 8x * 0.25) + -7 9 + 0.5x = (3.5 + 2x) + -7 Reorder the terms: 9 + 0.5x = 3.5 + -7 + 2x Combine like terms: 3.5 + -7 = -3.5 9 + 0.5x = -3.5 + 2x Solving 9 + 0.5x = -3.5 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. 9 + 0.5x + -2x = -3.5 + 2x + -2x Combine like terms: 0.5x + -2x = -1.5x 9 + -1.5x = -3.5 + 2x + -2x Combine like terms: 2x + -2x = 0 9 + -1.5x = -3.5 + 0 9 + -1.5x = -3.5 Add '-9' to each side of the equation. 9 + -9 + -1.5x = -3.5 + -9 Combine like terms: 9 + -9 = 0 0 + -1.5x = -3.5 + -9 -1.5x = -3.5 + -9 Combine like terms: -3.5 + -9 = -12.5 -1.5x = -12.5 Divide each side by '-1.5'. x = 8.333333333 Simplifying x = 8.333333333
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