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Simplifying 1.5x + 2.5(x + 2) = 0.5(x + -5) + 1.5x + 3.5 Reorder the terms: 1.5x + 2.5(2 + x) = 0.5(x + -5) + 1.5x + 3.5 1.5x + (2 * 2.5 + x * 2.5) = 0.5(x + -5) + 1.5x + 3.5 1.5x + (5 + 2.5x) = 0.5(x + -5) + 1.5x + 3.5 Reorder the terms: 5 + 1.5x + 2.5x = 0.5(x + -5) + 1.5x + 3.5 Combine like terms: 1.5x + 2.5x = 4x 5 + 4x = 0.5(x + -5) + 1.5x + 3.5 Reorder the terms: 5 + 4x = 0.5(-5 + x) + 1.5x + 3.5 5 + 4x = (-5 * 0.5 + x * 0.5) + 1.5x + 3.5 5 + 4x = (-2.5 + 0.5x) + 1.5x + 3.5 Reorder the terms: 5 + 4x = -2.5 + 3.5 + 0.5x + 1.5x Combine like terms: -2.5 + 3.5 = 1 5 + 4x = 1 + 0.5x + 1.5x Combine like terms: 0.5x + 1.5x = 2x 5 + 4x = 1 + 2x Solving 5 + 4x = 1 + 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. 5 + 4x + -2x = 1 + 2x + -2x Combine like terms: 4x + -2x = 2x 5 + 2x = 1 + 2x + -2x Combine like terms: 2x + -2x = 0 5 + 2x = 1 + 0 5 + 2x = 1 Add '-5' to each side of the equation. 5 + -5 + 2x = 1 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 1 + -5 2x = 1 + -5 Combine like terms: 1 + -5 = -4 2x = -4 Divide each side by '2'. x = -2 Simplifying x = -2
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