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Simplifying 0.01(x + -0.9) + 0.04(3x + -23) = 0.5(4x + 0.012) Reorder the terms: 0.01(-0.9 + x) + 0.04(3x + -23) = 0.5(4x + 0.012) (-0.9 * 0.01 + x * 0.01) + 0.04(3x + -23) = 0.5(4x + 0.012) (-0.009 + 0.01x) + 0.04(3x + -23) = 0.5(4x + 0.012) Reorder the terms: -0.009 + 0.01x + 0.04(-23 + 3x) = 0.5(4x + 0.012) -0.009 + 0.01x + (-23 * 0.04 + 3x * 0.04) = 0.5(4x + 0.012) -0.009 + 0.01x + (-0.92 + 0.12x) = 0.5(4x + 0.012) Reorder the terms: -0.009 + -0.92 + 0.01x + 0.12x = 0.5(4x + 0.012) Combine like terms: -0.009 + -0.92 = -0.929 -0.929 + 0.01x + 0.12x = 0.5(4x + 0.012) Combine like terms: 0.01x + 0.12x = 0.13x -0.929 + 0.13x = 0.5(4x + 0.012) Reorder the terms: -0.929 + 0.13x = 0.5(0.012 + 4x) -0.929 + 0.13x = (0.012 * 0.5 + 4x * 0.5) -0.929 + 0.13x = (0.006 + 2x) Solving -0.929 + 0.13x = 0.006 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -0.929 + 0.13x + -2x = 0.006 + 2x + -2x Combine like terms: 0.13x + -2x = -1.87x -0.929 + -1.87x = 0.006 + 2x + -2x Combine like terms: 2x + -2x = 0 -0.929 + -1.87x = 0.006 + 0 -0.929 + -1.87x = 0.006 Add '0.929' to each side of the equation. -0.929 + 0.929 + -1.87x = 0.006 + 0.929 Combine like terms: -0.929 + 0.929 = 0.000 0.000 + -1.87x = 0.006 + 0.929 -1.87x = 0.006 + 0.929 Combine like terms: 0.006 + 0.929 = 0.935 -1.87x = 0.935 Divide each side by '-1.87'. x = -0.5 Simplifying x = -0.5
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