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Simplifying 12(3x + 4) + -7(2x + -2) = 2x + -78 Reorder the terms: 12(4 + 3x) + -7(2x + -2) = 2x + -78 (4 * 12 + 3x * 12) + -7(2x + -2) = 2x + -78 (48 + 36x) + -7(2x + -2) = 2x + -78 Reorder the terms: 48 + 36x + -7(-2 + 2x) = 2x + -78 48 + 36x + (-2 * -7 + 2x * -7) = 2x + -78 48 + 36x + (14 + -14x) = 2x + -78 Reorder the terms: 48 + 14 + 36x + -14x = 2x + -78 Combine like terms: 48 + 14 = 62 62 + 36x + -14x = 2x + -78 Combine like terms: 36x + -14x = 22x 62 + 22x = 2x + -78 Reorder the terms: 62 + 22x = -78 + 2x Solving 62 + 22x = -78 + 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. 62 + 22x + -2x = -78 + 2x + -2x Combine like terms: 22x + -2x = 20x 62 + 20x = -78 + 2x + -2x Combine like terms: 2x + -2x = 0 62 + 20x = -78 + 0 62 + 20x = -78 Add '-62' to each side of the equation. 62 + -62 + 20x = -78 + -62 Combine like terms: 62 + -62 = 0 0 + 20x = -78 + -62 20x = -78 + -62 Combine like terms: -78 + -62 = -140 20x = -140 Divide each side by '20'. x = -7 Simplifying x = -7
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