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Simplifying 5x + -3 + 10x + -12 + 2(2x + 3) = 12(x + -1) + -5(6 + -2x) Reorder the terms: 5x + -3 + 10x + -12 + 2(3 + 2x) = 12(x + -1) + -5(6 + -2x) 5x + -3 + 10x + -12 + (3 * 2 + 2x * 2) = 12(x + -1) + -5(6 + -2x) 5x + -3 + 10x + -12 + (6 + 4x) = 12(x + -1) + -5(6 + -2x) Reorder the terms: -3 + -12 + 6 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: -3 + -12 = -15 -15 + 6 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: -15 + 6 = -9 -9 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: 5x + 10x = 15x -9 + 15x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: 15x + 4x = 19x -9 + 19x = 12(x + -1) + -5(6 + -2x) Reorder the terms: -9 + 19x = 12(-1 + x) + -5(6 + -2x) -9 + 19x = (-1 * 12 + x * 12) + -5(6 + -2x) -9 + 19x = (-12 + 12x) + -5(6 + -2x) -9 + 19x = -12 + 12x + (6 * -5 + -2x * -5) -9 + 19x = -12 + 12x + (-30 + 10x) Reorder the terms: -9 + 19x = -12 + -30 + 12x + 10x Combine like terms: -12 + -30 = -42 -9 + 19x = -42 + 12x + 10x Combine like terms: 12x + 10x = 22x -9 + 19x = -42 + 22x Solving -9 + 19x = -42 + 22x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22x' to each side of the equation. -9 + 19x + -22x = -42 + 22x + -22x Combine like terms: 19x + -22x = -3x -9 + -3x = -42 + 22x + -22x Combine like terms: 22x + -22x = 0 -9 + -3x = -42 + 0 -9 + -3x = -42 Add '9' to each side of the equation. -9 + 9 + -3x = -42 + 9 Combine like terms: -9 + 9 = 0 0 + -3x = -42 + 9 -3x = -42 + 9 Combine like terms: -42 + 9 = -33 -3x = -33 Divide each side by '-3'. x = 11 Simplifying x = 11
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