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Simplifying 0.5(x + 2) = 0.1x + 0.6(x + -3) Reorder the terms: 0.5(2 + x) = 0.1x + 0.6(x + -3) (2 * 0.5 + x * 0.5) = 0.1x + 0.6(x + -3) (1 + 0.5x) = 0.1x + 0.6(x + -3) Reorder the terms: 1 + 0.5x = 0.1x + 0.6(-3 + x) 1 + 0.5x = 0.1x + (-3 * 0.6 + x * 0.6) 1 + 0.5x = 0.1x + (-1.8 + 0.6x) Reorder the terms: 1 + 0.5x = -1.8 + 0.1x + 0.6x Combine like terms: 0.1x + 0.6x = 0.7x 1 + 0.5x = -1.8 + 0.7x Solving 1 + 0.5x = -1.8 + 0.7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7x' to each side of the equation. 1 + 0.5x + -0.7x = -1.8 + 0.7x + -0.7x Combine like terms: 0.5x + -0.7x = -0.2x 1 + -0.2x = -1.8 + 0.7x + -0.7x Combine like terms: 0.7x + -0.7x = 0.0 1 + -0.2x = -1.8 + 0.0 1 + -0.2x = -1.8 Add '-1' to each side of the equation. 1 + -1 + -0.2x = -1.8 + -1 Combine like terms: 1 + -1 = 0 0 + -0.2x = -1.8 + -1 -0.2x = -1.8 + -1 Combine like terms: -1.8 + -1 = -2.8 -0.2x = -2.8 Divide each side by '-0.2'. x = 14 Simplifying x = 14
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