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Simplifying 2(3x + 4) + -5(1 + -2x) = 7(2x + -3) + 12 Reorder the terms: 2(4 + 3x) + -5(1 + -2x) = 7(2x + -3) + 12 (4 * 2 + 3x * 2) + -5(1 + -2x) = 7(2x + -3) + 12 (8 + 6x) + -5(1 + -2x) = 7(2x + -3) + 12 8 + 6x + (1 * -5 + -2x * -5) = 7(2x + -3) + 12 8 + 6x + (-5 + 10x) = 7(2x + -3) + 12 Reorder the terms: 8 + -5 + 6x + 10x = 7(2x + -3) + 12 Combine like terms: 8 + -5 = 3 3 + 6x + 10x = 7(2x + -3) + 12 Combine like terms: 6x + 10x = 16x 3 + 16x = 7(2x + -3) + 12 Reorder the terms: 3 + 16x = 7(-3 + 2x) + 12 3 + 16x = (-3 * 7 + 2x * 7) + 12 3 + 16x = (-21 + 14x) + 12 Reorder the terms: 3 + 16x = -21 + 12 + 14x Combine like terms: -21 + 12 = -9 3 + 16x = -9 + 14x Solving 3 + 16x = -9 + 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. 3 + 16x + -14x = -9 + 14x + -14x Combine like terms: 16x + -14x = 2x 3 + 2x = -9 + 14x + -14x Combine like terms: 14x + -14x = 0 3 + 2x = -9 + 0 3 + 2x = -9 Add '-3' to each side of the equation. 3 + -3 + 2x = -9 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = -9 + -3 2x = -9 + -3 Combine like terms: -9 + -3 = -12 2x = -12 Divide each side by '2'. x = -6 Simplifying x = -6
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