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Simplifying 0.8(x + -5) + 0.5 = 1 + -0.3(10 + -2x) + -0.5 Reorder the terms: 0.8(-5 + x) + 0.5 = 1 + -0.3(10 + -2x) + -0.5 (-5 * 0.8 + x * 0.8) + 0.5 = 1 + -0.3(10 + -2x) + -0.5 (-4 + 0.8x) + 0.5 = 1 + -0.3(10 + -2x) + -0.5 Reorder the terms: -4 + 0.5 + 0.8x = 1 + -0.3(10 + -2x) + -0.5 Combine like terms: -4 + 0.5 = -3.5 -3.5 + 0.8x = 1 + -0.3(10 + -2x) + -0.5 -3.5 + 0.8x = 1 + (10 * -0.3 + -2x * -0.3) + -0.5 -3.5 + 0.8x = 1 + (-3 + 0.6x) + -0.5 Reorder the terms: -3.5 + 0.8x = 1 + -3 + -0.5 + 0.6x Combine like terms: 1 + -3 = -2 -3.5 + 0.8x = -2 + -0.5 + 0.6x Combine like terms: -2 + -0.5 = -2.5 -3.5 + 0.8x = -2.5 + 0.6x Solving -3.5 + 0.8x = -2.5 + 0.6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6x' to each side of the equation. -3.5 + 0.8x + -0.6x = -2.5 + 0.6x + -0.6x Combine like terms: 0.8x + -0.6x = 0.2x -3.5 + 0.2x = -2.5 + 0.6x + -0.6x Combine like terms: 0.6x + -0.6x = 0.0 -3.5 + 0.2x = -2.5 + 0.0 -3.5 + 0.2x = -2.5 Add '3.5' to each side of the equation. -3.5 + 3.5 + 0.2x = -2.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.2x = -2.5 + 3.5 0.2x = -2.5 + 3.5 Combine like terms: -2.5 + 3.5 = 1 0.2x = 1 Divide each side by '0.2'. x = 5 Simplifying x = 5
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