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Simplifying 10 + 2(3x + -8) = 12(1 + x) + -2(1 + -1x) Reorder the terms: 10 + 2(-8 + 3x) = 12(1 + x) + -2(1 + -1x) 10 + (-8 * 2 + 3x * 2) = 12(1 + x) + -2(1 + -1x) 10 + (-16 + 6x) = 12(1 + x) + -2(1 + -1x) Combine like terms: 10 + -16 = -6 -6 + 6x = 12(1 + x) + -2(1 + -1x) -6 + 6x = (1 * 12 + x * 12) + -2(1 + -1x) -6 + 6x = (12 + 12x) + -2(1 + -1x) -6 + 6x = 12 + 12x + (1 * -2 + -1x * -2) -6 + 6x = 12 + 12x + (-2 + 2x) Reorder the terms: -6 + 6x = 12 + -2 + 12x + 2x Combine like terms: 12 + -2 = 10 -6 + 6x = 10 + 12x + 2x Combine like terms: 12x + 2x = 14x -6 + 6x = 10 + 14x Solving -6 + 6x = 10 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. -6 + 6x + -14x = 10 + 14x + -14x Combine like terms: 6x + -14x = -8x -6 + -8x = 10 + 14x + -14x Combine like terms: 14x + -14x = 0 -6 + -8x = 10 + 0 -6 + -8x = 10 Add '6' to each side of the equation. -6 + 6 + -8x = 10 + 6 Combine like terms: -6 + 6 = 0 0 + -8x = 10 + 6 -8x = 10 + 6 Combine like terms: 10 + 6 = 16 -8x = 16 Divide each side by '-8'. x = -2 Simplifying x = -2
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