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Simplifying 3(x + -7) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10) Reorder the terms: 3(-7 + x) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10) (-7 * 3 + x * 3) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10) (-21 + 3x) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10) -21 + 3x + (9 * -1 + -2x * -1) = 2(12 + -1x) + -1(x + -10) -21 + 3x + (-9 + 2x) = 2(12 + -1x) + -1(x + -10) Reorder the terms: -21 + -9 + 3x + 2x = 2(12 + -1x) + -1(x + -10) Combine like terms: -21 + -9 = -30 -30 + 3x + 2x = 2(12 + -1x) + -1(x + -10) Combine like terms: 3x + 2x = 5x -30 + 5x = 2(12 + -1x) + -1(x + -10) -30 + 5x = (12 * 2 + -1x * 2) + -1(x + -10) -30 + 5x = (24 + -2x) + -1(x + -10) Reorder the terms: -30 + 5x = 24 + -2x + -1(-10 + x) -30 + 5x = 24 + -2x + (-10 * -1 + x * -1) -30 + 5x = 24 + -2x + (10 + -1x) Reorder the terms: -30 + 5x = 24 + 10 + -2x + -1x Combine like terms: 24 + 10 = 34 -30 + 5x = 34 + -2x + -1x Combine like terms: -2x + -1x = -3x -30 + 5x = 34 + -3x Solving -30 + 5x = 34 + -3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3x' to each side of the equation. -30 + 5x + 3x = 34 + -3x + 3x Combine like terms: 5x + 3x = 8x -30 + 8x = 34 + -3x + 3x Combine like terms: -3x + 3x = 0 -30 + 8x = 34 + 0 -30 + 8x = 34 Add '30' to each side of the equation. -30 + 30 + 8x = 34 + 30 Combine like terms: -30 + 30 = 0 0 + 8x = 34 + 30 8x = 34 + 30 Combine like terms: 34 + 30 = 64 8x = 64 Divide each side by '8'. x = 8 Simplifying x = 8
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