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Simplifying 2(x + -7) + -3(x + 2) = 4(x + 3) + 2(x + -9) Reorder the terms: 2(-7 + x) + -3(x + 2) = 4(x + 3) + 2(x + -9) (-7 * 2 + x * 2) + -3(x + 2) = 4(x + 3) + 2(x + -9) (-14 + 2x) + -3(x + 2) = 4(x + 3) + 2(x + -9) Reorder the terms: -14 + 2x + -3(2 + x) = 4(x + 3) + 2(x + -9) -14 + 2x + (2 * -3 + x * -3) = 4(x + 3) + 2(x + -9) -14 + 2x + (-6 + -3x) = 4(x + 3) + 2(x + -9) Reorder the terms: -14 + -6 + 2x + -3x = 4(x + 3) + 2(x + -9) Combine like terms: -14 + -6 = -20 -20 + 2x + -3x = 4(x + 3) + 2(x + -9) Combine like terms: 2x + -3x = -1x -20 + -1x = 4(x + 3) + 2(x + -9) Reorder the terms: -20 + -1x = 4(3 + x) + 2(x + -9) -20 + -1x = (3 * 4 + x * 4) + 2(x + -9) -20 + -1x = (12 + 4x) + 2(x + -9) Reorder the terms: -20 + -1x = 12 + 4x + 2(-9 + x) -20 + -1x = 12 + 4x + (-9 * 2 + x * 2) -20 + -1x = 12 + 4x + (-18 + 2x) Reorder the terms: -20 + -1x = 12 + -18 + 4x + 2x Combine like terms: 12 + -18 = -6 -20 + -1x = -6 + 4x + 2x Combine like terms: 4x + 2x = 6x -20 + -1x = -6 + 6x Solving -20 + -1x = -6 + 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. -20 + -1x + -6x = -6 + 6x + -6x Combine like terms: -1x + -6x = -7x -20 + -7x = -6 + 6x + -6x Combine like terms: 6x + -6x = 0 -20 + -7x = -6 + 0 -20 + -7x = -6 Add '20' to each side of the equation. -20 + 20 + -7x = -6 + 20 Combine like terms: -20 + 20 = 0 0 + -7x = -6 + 20 -7x = -6 + 20 Combine like terms: -6 + 20 = 14 -7x = 14 Divide each side by '-7'. x = -2 Simplifying x = -2
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