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Simplifying 12 + -3(x + -4) + 11(x + 2) = 102 Reorder the terms: 12 + -3(-4 + x) + 11(x + 2) = 102 12 + (-4 * -3 + x * -3) + 11(x + 2) = 102 12 + (12 + -3x) + 11(x + 2) = 102 Reorder the terms: 12 + 12 + -3x + 11(2 + x) = 102 12 + 12 + -3x + (2 * 11 + x * 11) = 102 12 + 12 + -3x + (22 + 11x) = 102 Reorder the terms: 12 + 12 + 22 + -3x + 11x = 102 Combine like terms: 12 + 12 = 24 24 + 22 + -3x + 11x = 102 Combine like terms: 24 + 22 = 46 46 + -3x + 11x = 102 Combine like terms: -3x + 11x = 8x 46 + 8x = 102 Solving 46 + 8x = 102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + 8x = 102 + -46 Combine like terms: 46 + -46 = 0 0 + 8x = 102 + -46 8x = 102 + -46 Combine like terms: 102 + -46 = 56 8x = 56 Divide each side by '8'. x = 7 Simplifying x = 7
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