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Simplifying 2(4x + 1) + -4(5 + -1x) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) Reorder the terms: 2(1 + 4x) + -4(5 + -1x) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) (1 * 2 + 4x * 2) + -4(5 + -1x) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) (2 + 8x) + -4(5 + -1x) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) 2 + 8x + (5 * -4 + -1x * -4) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) 2 + 8x + (-20 + 4x) + -5 = 2(10 + -1x) + -12 + 3(5x + -7) Reorder the terms: 2 + -20 + -5 + 8x + 4x = 2(10 + -1x) + -12 + 3(5x + -7) Combine like terms: 2 + -20 = -18 -18 + -5 + 8x + 4x = 2(10 + -1x) + -12 + 3(5x + -7) Combine like terms: -18 + -5 = -23 -23 + 8x + 4x = 2(10 + -1x) + -12 + 3(5x + -7) Combine like terms: 8x + 4x = 12x -23 + 12x = 2(10 + -1x) + -12 + 3(5x + -7) -23 + 12x = (10 * 2 + -1x * 2) + -12 + 3(5x + -7) -23 + 12x = (20 + -2x) + -12 + 3(5x + -7) Reorder the terms: -23 + 12x = 20 + -2x + -12 + 3(-7 + 5x) -23 + 12x = 20 + -2x + -12 + (-7 * 3 + 5x * 3) -23 + 12x = 20 + -2x + -12 + (-21 + 15x) Reorder the terms: -23 + 12x = 20 + -12 + -21 + -2x + 15x Combine like terms: 20 + -12 = 8 -23 + 12x = 8 + -21 + -2x + 15x Combine like terms: 8 + -21 = -13 -23 + 12x = -13 + -2x + 15x Combine like terms: -2x + 15x = 13x -23 + 12x = -13 + 13x Solving -23 + 12x = -13 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. -23 + 12x + -13x = -13 + 13x + -13x Combine like terms: 12x + -13x = -1x -23 + -1x = -13 + 13x + -13x Combine like terms: 13x + -13x = 0 -23 + -1x = -13 + 0 -23 + -1x = -13 Add '23' to each side of the equation. -23 + 23 + -1x = -13 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = -13 + 23 -1x = -13 + 23 Combine like terms: -13 + 23 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10
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