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Simplifying 12(3x + 4) + -5(2x + -2) = 6x + -82 Reorder the terms: 12(4 + 3x) + -5(2x + -2) = 6x + -82 (4 * 12 + 3x * 12) + -5(2x + -2) = 6x + -82 (48 + 36x) + -5(2x + -2) = 6x + -82 Reorder the terms: 48 + 36x + -5(-2 + 2x) = 6x + -82 48 + 36x + (-2 * -5 + 2x * -5) = 6x + -82 48 + 36x + (10 + -10x) = 6x + -82 Reorder the terms: 48 + 10 + 36x + -10x = 6x + -82 Combine like terms: 48 + 10 = 58 58 + 36x + -10x = 6x + -82 Combine like terms: 36x + -10x = 26x 58 + 26x = 6x + -82 Reorder the terms: 58 + 26x = -82 + 6x Solving 58 + 26x = -82 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 58 + 26x + -6x = -82 + 6x + -6x Combine like terms: 26x + -6x = 20x 58 + 20x = -82 + 6x + -6x Combine like terms: 6x + -6x = 0 58 + 20x = -82 + 0 58 + 20x = -82 Add '-58' to each side of the equation. 58 + -58 + 20x = -82 + -58 Combine like terms: 58 + -58 = 0 0 + 20x = -82 + -58 20x = -82 + -58 Combine like terms: -82 + -58 = -140 20x = -140 Divide each side by '20'. x = -7 Simplifying x = -7
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