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Simplifying 0.9(-3x + 5) + 0.6(9x + -7.5) = 18(1.5x + -0.2) + 3.6 Reorder the terms: 0.9(5 + -3x) + 0.6(9x + -7.5) = 18(1.5x + -0.2) + 3.6 (5 * 0.9 + -3x * 0.9) + 0.6(9x + -7.5) = 18(1.5x + -0.2) + 3.6 (4.5 + -2.7x) + 0.6(9x + -7.5) = 18(1.5x + -0.2) + 3.6 Reorder the terms: 4.5 + -2.7x + 0.6(-7.5 + 9x) = 18(1.5x + -0.2) + 3.6 4.5 + -2.7x + (-7.5 * 0.6 + 9x * 0.6) = 18(1.5x + -0.2) + 3.6 4.5 + -2.7x + (-4.5 + 5.4x) = 18(1.5x + -0.2) + 3.6 Reorder the terms: 4.5 + -4.5 + -2.7x + 5.4x = 18(1.5x + -0.2) + 3.6 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -2.7x + 5.4x = 18(1.5x + -0.2) + 3.6 -2.7x + 5.4x = 18(1.5x + -0.2) + 3.6 Combine like terms: -2.7x + 5.4x = 2.7x 2.7x = 18(1.5x + -0.2) + 3.6 Reorder the terms: 2.7x = 18(-0.2 + 1.5x) + 3.6 2.7x = (-0.2 * 18 + 1.5x * 18) + 3.6 2.7x = (-3.6 + 27x) + 3.6 Reorder the terms: 2.7x = -3.6 + 3.6 + 27x Combine like terms: -3.6 + 3.6 = 0.0 2.7x = 0.0 + 27x 2.7x = 27x Solving 2.7x = 27x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27x' to each side of the equation. 2.7x + -27x = 27x + -27x Combine like terms: 2.7x + -27x = -24.3x -24.3x = 27x + -27x Combine like terms: 27x + -27x = 0 -24.3x = 0 Divide each side by '-24.3'. x = 0 Simplifying x = 0
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