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Simplifying 5(x + -3) + 10x + -12 + 2(2x + 3) = 12(x + -1) + -5(6 + -2x) Reorder the terms: 5(-3 + x) + 10x + -12 + 2(2x + 3) = 12(x + -1) + -5(6 + -2x) (-3 * 5 + x * 5) + 10x + -12 + 2(2x + 3) = 12(x + -1) + -5(6 + -2x) (-15 + 5x) + 10x + -12 + 2(2x + 3) = 12(x + -1) + -5(6 + -2x) Reorder the terms: -15 + 5x + 10x + -12 + 2(3 + 2x) = 12(x + -1) + -5(6 + -2x) -15 + 5x + 10x + -12 + (3 * 2 + 2x * 2) = 12(x + -1) + -5(6 + -2x) -15 + 5x + 10x + -12 + (6 + 4x) = 12(x + -1) + -5(6 + -2x) Reorder the terms: -15 + -12 + 6 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: -15 + -12 = -27 -27 + 6 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: -27 + 6 = -21 -21 + 5x + 10x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: 5x + 10x = 15x -21 + 15x + 4x = 12(x + -1) + -5(6 + -2x) Combine like terms: 15x + 4x = 19x -21 + 19x = 12(x + -1) + -5(6 + -2x) Reorder the terms: -21 + 19x = 12(-1 + x) + -5(6 + -2x) -21 + 19x = (-1 * 12 + x * 12) + -5(6 + -2x) -21 + 19x = (-12 + 12x) + -5(6 + -2x) -21 + 19x = -12 + 12x + (6 * -5 + -2x * -5) -21 + 19x = -12 + 12x + (-30 + 10x) Reorder the terms: -21 + 19x = -12 + -30 + 12x + 10x Combine like terms: -12 + -30 = -42 -21 + 19x = -42 + 12x + 10x Combine like terms: 12x + 10x = 22x -21 + 19x = -42 + 22x Solving -21 + 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. -21 + 19x + -22x = -42 + 22x + -22x Combine like terms: 19x + -22x = -3x -21 + -3x = -42 + 22x + -22x Combine like terms: 22x + -22x = 0 -21 + -3x = -42 + 0 -21 + -3x = -42 Add '21' to each side of the equation. -21 + 21 + -3x = -42 + 21 Combine like terms: -21 + 21 = 0 0 + -3x = -42 + 21 -3x = -42 + 21 Combine like terms: -42 + 21 = -21 -3x = -21 Divide each side by '-3'. x = 7 Simplifying x = 7
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