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Simplifying 0.2(x + 8) = 0.25(x + -3) + 1 Reorder the terms: 0.2(8 + x) = 0.25(x + -3) + 1 (8 * 0.2 + x * 0.2) = 0.25(x + -3) + 1 (1.6 + 0.2x) = 0.25(x + -3) + 1 Reorder the terms: 1.6 + 0.2x = 0.25(-3 + x) + 1 1.6 + 0.2x = (-3 * 0.25 + x * 0.25) + 1 1.6 + 0.2x = (-0.75 + 0.25x) + 1 Reorder the terms: 1.6 + 0.2x = -0.75 + 1 + 0.25x Combine like terms: -0.75 + 1 = 0.25 1.6 + 0.2x = 0.25 + 0.25x Solving 1.6 + 0.2x = 0.25 + 0.25x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25x' to each side of the equation. 1.6 + 0.2x + -0.25x = 0.25 + 0.25x + -0.25x Combine like terms: 0.2x + -0.25x = -0.05x 1.6 + -0.05x = 0.25 + 0.25x + -0.25x Combine like terms: 0.25x + -0.25x = 0.00 1.6 + -0.05x = 0.25 + 0.00 1.6 + -0.05x = 0.25 Add '-1.6' to each side of the equation. 1.6 + -1.6 + -0.05x = 0.25 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -0.05x = 0.25 + -1.6 -0.05x = 0.25 + -1.6 Combine like terms: 0.25 + -1.6 = -1.35 -0.05x = -1.35 Divide each side by '-0.05'. x = 27 Simplifying x = 27
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