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Simplifying 0.6(x + -1) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 Reorder the terms: 0.6(-1 + x) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 (-1 * 0.6 + x * 0.6) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 (-0.6 + 0.6x) + 0.5 = 1 + -0.4(2 + -2x) + -0.5 Reorder the terms: -0.6 + 0.5 + 0.6x = 1 + -0.4(2 + -2x) + -0.5 Combine like terms: -0.6 + 0.5 = -0.1 -0.1 + 0.6x = 1 + -0.4(2 + -2x) + -0.5 -0.1 + 0.6x = 1 + (2 * -0.4 + -2x * -0.4) + -0.5 -0.1 + 0.6x = 1 + (-0.8 + 0.8x) + -0.5 Reorder the terms: -0.1 + 0.6x = 1 + -0.8 + -0.5 + 0.8x Combine like terms: 1 + -0.8 = 0.2 -0.1 + 0.6x = 0.2 + -0.5 + 0.8x Combine like terms: 0.2 + -0.5 = -0.3 -0.1 + 0.6x = -0.3 + 0.8x Solving -0.1 + 0.6x = -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. -0.1 + 0.6x + -0.8x = -0.3 + 0.8x + -0.8x Combine like terms: 0.6x + -0.8x = -0.2x -0.1 + -0.2x = -0.3 + 0.8x + -0.8x Combine like terms: 0.8x + -0.8x = 0.0 -0.1 + -0.2x = -0.3 + 0.0 -0.1 + -0.2x = -0.3 Add '0.1' to each side of the equation. -0.1 + 0.1 + -0.2x = -0.3 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.2x = -0.3 + 0.1 -0.2x = -0.3 + 0.1 Combine like terms: -0.3 + 0.1 = -0.2 -0.2x = -0.2 Divide each side by '-0.2'. x = 1 Simplifying x = 1
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