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Simplifying 0.8(x + -0.5) + 0.5x = 0.9(x + -0.4) + -3.56 Reorder the terms: 0.8(-0.5 + x) + 0.5x = 0.9(x + -0.4) + -3.56 (-0.5 * 0.8 + x * 0.8) + 0.5x = 0.9(x + -0.4) + -3.56 (-0.4 + 0.8x) + 0.5x = 0.9(x + -0.4) + -3.56 Combine like terms: 0.8x + 0.5x = 1.3x -0.4 + 1.3x = 0.9(x + -0.4) + -3.56 Reorder the terms: -0.4 + 1.3x = 0.9(-0.4 + x) + -3.56 -0.4 + 1.3x = (-0.4 * 0.9 + x * 0.9) + -3.56 -0.4 + 1.3x = (-0.36 + 0.9x) + -3.56 Reorder the terms: -0.4 + 1.3x = -0.36 + -3.56 + 0.9x Combine like terms: -0.36 + -3.56 = -3.92 -0.4 + 1.3x = -3.92 + 0.9x Solving -0.4 + 1.3x = -3.92 + 0.9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9x' to each side of the equation. -0.4 + 1.3x + -0.9x = -3.92 + 0.9x + -0.9x Combine like terms: 1.3x + -0.9x = 0.4x -0.4 + 0.4x = -3.92 + 0.9x + -0.9x Combine like terms: 0.9x + -0.9x = 0.0 -0.4 + 0.4x = -3.92 + 0.0 -0.4 + 0.4x = -3.92 Add '0.4' to each side of the equation. -0.4 + 0.4 + 0.4x = -3.92 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.4x = -3.92 + 0.4 0.4x = -3.92 + 0.4 Combine like terms: -3.92 + 0.4 = -3.52 0.4x = -3.52 Divide each side by '0.4'. x = -8.8 Simplifying x = -8.8
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