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Simplifying 0.05(x + -0.1) + 0.03(2x + -2) = 0.4(3x + 0.11) Reorder the terms: 0.05(-0.1 + x) + 0.03(2x + -2) = 0.4(3x + 0.11) (-0.1 * 0.05 + x * 0.05) + 0.03(2x + -2) = 0.4(3x + 0.11) (-0.005 + 0.05x) + 0.03(2x + -2) = 0.4(3x + 0.11) Reorder the terms: -0.005 + 0.05x + 0.03(-2 + 2x) = 0.4(3x + 0.11) -0.005 + 0.05x + (-2 * 0.03 + 2x * 0.03) = 0.4(3x + 0.11) -0.005 + 0.05x + (-0.06 + 0.06x) = 0.4(3x + 0.11) Reorder the terms: -0.005 + -0.06 + 0.05x + 0.06x = 0.4(3x + 0.11) Combine like terms: -0.005 + -0.06 = -0.065 -0.065 + 0.05x + 0.06x = 0.4(3x + 0.11) Combine like terms: 0.05x + 0.06x = 0.11x -0.065 + 0.11x = 0.4(3x + 0.11) Reorder the terms: -0.065 + 0.11x = 0.4(0.11 + 3x) -0.065 + 0.11x = (0.11 * 0.4 + 3x * 0.4) -0.065 + 0.11x = (0.044 + 1.2x) Solving -0.065 + 0.11x = 0.044 + 1.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2x' to each side of the equation. -0.065 + 0.11x + -1.2x = 0.044 + 1.2x + -1.2x Combine like terms: 0.11x + -1.2x = -1.09x -0.065 + -1.09x = 0.044 + 1.2x + -1.2x Combine like terms: 1.2x + -1.2x = 0.0 -0.065 + -1.09x = 0.044 + 0.0 -0.065 + -1.09x = 0.044 Add '0.065' to each side of the equation. -0.065 + 0.065 + -1.09x = 0.044 + 0.065 Combine like terms: -0.065 + 0.065 = 0.000 0.000 + -1.09x = 0.044 + 0.065 -1.09x = 0.044 + 0.065 Combine like terms: 0.044 + 0.065 = 0.109 -1.09x = 0.109 Divide each side by '-1.09'. x = -0.1 Simplifying x = -0.1
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