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Simplifying 3(x + 2) + -4(x + -3) = 2(3x + -1) + -3(2x + -4) Reorder the terms: 3(2 + x) + -4(x + -3) = 2(3x + -1) + -3(2x + -4) (2 * 3 + x * 3) + -4(x + -3) = 2(3x + -1) + -3(2x + -4) (6 + 3x) + -4(x + -3) = 2(3x + -1) + -3(2x + -4) Reorder the terms: 6 + 3x + -4(-3 + x) = 2(3x + -1) + -3(2x + -4) 6 + 3x + (-3 * -4 + x * -4) = 2(3x + -1) + -3(2x + -4) 6 + 3x + (12 + -4x) = 2(3x + -1) + -3(2x + -4) Reorder the terms: 6 + 12 + 3x + -4x = 2(3x + -1) + -3(2x + -4) Combine like terms: 6 + 12 = 18 18 + 3x + -4x = 2(3x + -1) + -3(2x + -4) Combine like terms: 3x + -4x = -1x 18 + -1x = 2(3x + -1) + -3(2x + -4) Reorder the terms: 18 + -1x = 2(-1 + 3x) + -3(2x + -4) 18 + -1x = (-1 * 2 + 3x * 2) + -3(2x + -4) 18 + -1x = (-2 + 6x) + -3(2x + -4) Reorder the terms: 18 + -1x = -2 + 6x + -3(-4 + 2x) 18 + -1x = -2 + 6x + (-4 * -3 + 2x * -3) 18 + -1x = -2 + 6x + (12 + -6x) Reorder the terms: 18 + -1x = -2 + 12 + 6x + -6x Combine like terms: -2 + 12 = 10 18 + -1x = 10 + 6x + -6x Combine like terms: 6x + -6x = 0 18 + -1x = 10 + 0 18 + -1x = 10 Solving 18 + -1x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 10 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 10 + -18 -1x = 10 + -18 Combine like terms: 10 + -18 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8
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