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Simplifying 0.5x + 0.4(x + 2) = 5 + -1.5(x + 1) Reorder the terms: 0.5x + 0.4(2 + x) = 5 + -1.5(x + 1) 0.5x + (2 * 0.4 + x * 0.4) = 5 + -1.5(x + 1) 0.5x + (0.8 + 0.4x) = 5 + -1.5(x + 1) Reorder the terms: 0.8 + 0.5x + 0.4x = 5 + -1.5(x + 1) Combine like terms: 0.5x + 0.4x = 0.9x 0.8 + 0.9x = 5 + -1.5(x + 1) Reorder the terms: 0.8 + 0.9x = 5 + -1.5(1 + x) 0.8 + 0.9x = 5 + (1 * -1.5 + x * -1.5) 0.8 + 0.9x = 5 + (-1.5 + -1.5x) Combine like terms: 5 + -1.5 = 3.5 0.8 + 0.9x = 3.5 + -1.5x Solving 0.8 + 0.9x = 3.5 + -1.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5x' to each side of the equation. 0.8 + 0.9x + 1.5x = 3.5 + -1.5x + 1.5x Combine like terms: 0.9x + 1.5x = 2.4x 0.8 + 2.4x = 3.5 + -1.5x + 1.5x Combine like terms: -1.5x + 1.5x = 0.0 0.8 + 2.4x = 3.5 + 0.0 0.8 + 2.4x = 3.5 Add '-0.8' to each side of the equation. 0.8 + -0.8 + 2.4x = 3.5 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 2.4x = 3.5 + -0.8 2.4x = 3.5 + -0.8 Combine like terms: 3.5 + -0.8 = 2.7 2.4x = 2.7 Divide each side by '2.4'. x = 1.125 Simplifying x = 1.125
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