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Simplifying 1.25(x + -1) = 0.5(3x + -1) + -1 Reorder the terms: 1.25(-1 + x) = 0.5(3x + -1) + -1 (-1 * 1.25 + x * 1.25) = 0.5(3x + -1) + -1 (-1.25 + 1.25x) = 0.5(3x + -1) + -1 Reorder the terms: -1.25 + 1.25x = 0.5(-1 + 3x) + -1 -1.25 + 1.25x = (-1 * 0.5 + 3x * 0.5) + -1 -1.25 + 1.25x = (-0.5 + 1.5x) + -1 Reorder the terms: -1.25 + 1.25x = -0.5 + -1 + 1.5x Combine like terms: -0.5 + -1 = -1.5 -1.25 + 1.25x = -1.5 + 1.5x Solving -1.25 + 1.25x = -1.5 + 1.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5x' to each side of the equation. -1.25 + 1.25x + -1.5x = -1.5 + 1.5x + -1.5x Combine like terms: 1.25x + -1.5x = -0.25x -1.25 + -0.25x = -1.5 + 1.5x + -1.5x Combine like terms: 1.5x + -1.5x = 0.0 -1.25 + -0.25x = -1.5 + 0.0 -1.25 + -0.25x = -1.5 Add '1.25' to each side of the equation. -1.25 + 1.25 + -0.25x = -1.5 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.25x = -1.5 + 1.25 -0.25x = -1.5 + 1.25 Combine like terms: -1.5 + 1.25 = -0.25 -0.25x = -0.25 Divide each side by '-0.25'. x = 1 Simplifying x = 1
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