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Simplifying 6(x + -1) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 Reorder the terms: 6(-1 + x) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 (-1 * 6 + x * 6) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 (-6 + 6x) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 Reorder the terms: -6 + 0.5 + 6x = 1 + -0.4(2 + -2x) + -0.5 Combine like terms: -6 + 0.5 = -5.5 -5.5 + 6x = 1 + -0.4(2 + -2x) + -0.5 -5.5 + 6x = 1 + (2 * -0.4 + -2x * -0.4) + -0.5 -5.5 + 6x = 1 + (-0.8 + 0.8x) + -0.5 Reorder the terms: -5.5 + 6x = 1 + -0.8 + -0.5 + 0.8x Combine like terms: 1 + -0.8 = 0.2 -5.5 + 6x = 0.2 + -0.5 + 0.8x Combine like terms: 0.2 + -0.5 = -0.3 -5.5 + 6x = -0.3 + 0.8x Solving -5.5 + 6x = -0.3 + 0.8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8x' to each side of the equation. -5.5 + 6x + -0.8x = -0.3 + 0.8x + -0.8x Combine like terms: 6x + -0.8x = 5.2x -5.5 + 5.2x = -0.3 + 0.8x + -0.8x Combine like terms: 0.8x + -0.8x = 0.0 -5.5 + 5.2x = -0.3 + 0.0 -5.5 + 5.2x = -0.3 Add '5.5' to each side of the equation. -5.5 + 5.5 + 5.2x = -0.3 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 5.2x = -0.3 + 5.5 5.2x = -0.3 + 5.5 Combine like terms: -0.3 + 5.5 = 5.2 5.2x = 5.2 Divide each side by '5.2'. x = 1 Simplifying x = 1
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