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Simplifying 0.4(x + -5) + 0.5 = 1 + -0.8(10 + -2x) + -0.5 Reorder the terms: 0.4(-5 + x) + 0.5 = 1 + -0.8(10 + -2x) + -0.5 (-5 * 0.4 + x * 0.4) + 0.5 = 1 + -0.8(10 + -2x) + -0.5 (-2 + 0.4x) + 0.5 = 1 + -0.8(10 + -2x) + -0.5 Reorder the terms: -2 + 0.5 + 0.4x = 1 + -0.8(10 + -2x) + -0.5 Combine like terms: -2 + 0.5 = -1.5 -1.5 + 0.4x = 1 + -0.8(10 + -2x) + -0.5 -1.5 + 0.4x = 1 + (10 * -0.8 + -2x * -0.8) + -0.5 -1.5 + 0.4x = 1 + (-8 + 1.6x) + -0.5 Reorder the terms: -1.5 + 0.4x = 1 + -8 + -0.5 + 1.6x Combine like terms: 1 + -8 = -7 -1.5 + 0.4x = -7 + -0.5 + 1.6x Combine like terms: -7 + -0.5 = -7.5 -1.5 + 0.4x = -7.5 + 1.6x Solving -1.5 + 0.4x = -7.5 + 1.6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6x' to each side of the equation. -1.5 + 0.4x + -1.6x = -7.5 + 1.6x + -1.6x Combine like terms: 0.4x + -1.6x = -1.2x -1.5 + -1.2x = -7.5 + 1.6x + -1.6x Combine like terms: 1.6x + -1.6x = 0.0 -1.5 + -1.2x = -7.5 + 0.0 -1.5 + -1.2x = -7.5 Add '1.5' to each side of the equation. -1.5 + 1.5 + -1.2x = -7.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.2x = -7.5 + 1.5 -1.2x = -7.5 + 1.5 Combine like terms: -7.5 + 1.5 = -6 -1.2x = -6 Divide each side by '-1.2'. x = 5 Simplifying x = 5
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