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Simplifying 4(3x + 2) + 2(x + 5) = 0.5(4x + -8) + -2 Reorder the terms: 4(2 + 3x) + 2(x + 5) = 0.5(4x + -8) + -2 (2 * 4 + 3x * 4) + 2(x + 5) = 0.5(4x + -8) + -2 (8 + 12x) + 2(x + 5) = 0.5(4x + -8) + -2 Reorder the terms: 8 + 12x + 2(5 + x) = 0.5(4x + -8) + -2 8 + 12x + (5 * 2 + x * 2) = 0.5(4x + -8) + -2 8 + 12x + (10 + 2x) = 0.5(4x + -8) + -2 Reorder the terms: 8 + 10 + 12x + 2x = 0.5(4x + -8) + -2 Combine like terms: 8 + 10 = 18 18 + 12x + 2x = 0.5(4x + -8) + -2 Combine like terms: 12x + 2x = 14x 18 + 14x = 0.5(4x + -8) + -2 Reorder the terms: 18 + 14x = 0.5(-8 + 4x) + -2 18 + 14x = (-8 * 0.5 + 4x * 0.5) + -2 18 + 14x = (-4 + 2x) + -2 Reorder the terms: 18 + 14x = -4 + -2 + 2x Combine like terms: -4 + -2 = -6 18 + 14x = -6 + 2x Solving 18 + 14x = -6 + 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. 18 + 14x + -2x = -6 + 2x + -2x Combine like terms: 14x + -2x = 12x 18 + 12x = -6 + 2x + -2x Combine like terms: 2x + -2x = 0 18 + 12x = -6 + 0 18 + 12x = -6 Add '-18' to each side of the equation. 18 + -18 + 12x = -6 + -18 Combine like terms: 18 + -18 = 0 0 + 12x = -6 + -18 12x = -6 + -18 Combine like terms: -6 + -18 = -24 12x = -24 Divide each side by '12'. x = -2 Simplifying x = -2
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