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Simplifying 0.5(4x + -6) + 3x + 2 = -2(0.5x + -4) + -1 Reorder the terms: 0.5(-6 + 4x) + 3x + 2 = -2(0.5x + -4) + -1 (-6 * 0.5 + 4x * 0.5) + 3x + 2 = -2(0.5x + -4) + -1 (-3 + 2x) + 3x + 2 = -2(0.5x + -4) + -1 Reorder the terms: -3 + 2 + 2x + 3x = -2(0.5x + -4) + -1 Combine like terms: -3 + 2 = -1 -1 + 2x + 3x = -2(0.5x + -4) + -1 Combine like terms: 2x + 3x = 5x -1 + 5x = -2(0.5x + -4) + -1 Reorder the terms: -1 + 5x = -2(-4 + 0.5x) + -1 -1 + 5x = (-4 * -2 + 0.5x * -2) + -1 -1 + 5x = (8 + -1x) + -1 Reorder the terms: -1 + 5x = 8 + -1 + -1x Combine like terms: 8 + -1 = 7 -1 + 5x = 7 + -1x Solving -1 + 5x = 7 + -1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'x' to each side of the equation. -1 + 5x + x = 7 + -1x + x Combine like terms: 5x + x = 6x -1 + 6x = 7 + -1x + x Combine like terms: -1x + x = 0 -1 + 6x = 7 + 0 -1 + 6x = 7 Add '1' to each side of the equation. -1 + 1 + 6x = 7 + 1 Combine like terms: -1 + 1 = 0 0 + 6x = 7 + 1 6x = 7 + 1 Combine like terms: 7 + 1 = 8 6x = 8 Divide each side by '6'. x = 1.333333333 Simplifying x = 1.333333333
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