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Simplifying 0.6(x + -5) + -0.5 = 1 + -0.1(10 + -2x) + -0.5 Reorder the terms: 0.6(-5 + x) + -0.5 = 1 + -0.1(10 + -2x) + -0.5 (-5 * 0.6 + x * 0.6) + -0.5 = 1 + -0.1(10 + -2x) + -0.5 (-3 + 0.6x) + -0.5 = 1 + -0.1(10 + -2x) + -0.5 Reorder the terms: -3 + -0.5 + 0.6x = 1 + -0.1(10 + -2x) + -0.5 Combine like terms: -3 + -0.5 = -3.5 -3.5 + 0.6x = 1 + -0.1(10 + -2x) + -0.5 -3.5 + 0.6x = 1 + (10 * -0.1 + -2x * -0.1) + -0.5 -3.5 + 0.6x = 1 + (-1 + 0.2x) + -0.5 Reorder the terms: -3.5 + 0.6x = 1 + -1 + -0.5 + 0.2x Combine like terms: 1 + -1 = 0 -3.5 + 0.6x = 0 + -0.5 + 0.2x -3.5 + 0.6x = -0.5 + 0.2x Solving -3.5 + 0.6x = -0.5 + 0.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2x' to each side of the equation. -3.5 + 0.6x + -0.2x = -0.5 + 0.2x + -0.2x Combine like terms: 0.6x + -0.2x = 0.4x -3.5 + 0.4x = -0.5 + 0.2x + -0.2x Combine like terms: 0.2x + -0.2x = 0.0 -3.5 + 0.4x = -0.5 + 0.0 -3.5 + 0.4x = -0.5 Add '3.5' to each side of the equation. -3.5 + 3.5 + 0.4x = -0.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.4x = -0.5 + 3.5 0.4x = -0.5 + 3.5 Combine like terms: -0.5 + 3.5 = 3 0.4x = 3 Divide each side by '0.4'. x = 7.5 Simplifying x = 7.5
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