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Simplifying 3(2x + 7) + 2(2x + 1) + -32 = 3(4x + -5) + 14 Reorder the terms: 3(7 + 2x) + 2(2x + 1) + -32 = 3(4x + -5) + 14 (7 * 3 + 2x * 3) + 2(2x + 1) + -32 = 3(4x + -5) + 14 (21 + 6x) + 2(2x + 1) + -32 = 3(4x + -5) + 14 Reorder the terms: 21 + 6x + 2(1 + 2x) + -32 = 3(4x + -5) + 14 21 + 6x + (1 * 2 + 2x * 2) + -32 = 3(4x + -5) + 14 21 + 6x + (2 + 4x) + -32 = 3(4x + -5) + 14 Reorder the terms: 21 + 2 + -32 + 6x + 4x = 3(4x + -5) + 14 Combine like terms: 21 + 2 = 23 23 + -32 + 6x + 4x = 3(4x + -5) + 14 Combine like terms: 23 + -32 = -9 -9 + 6x + 4x = 3(4x + -5) + 14 Combine like terms: 6x + 4x = 10x -9 + 10x = 3(4x + -5) + 14 Reorder the terms: -9 + 10x = 3(-5 + 4x) + 14 -9 + 10x = (-5 * 3 + 4x * 3) + 14 -9 + 10x = (-15 + 12x) + 14 Reorder the terms: -9 + 10x = -15 + 14 + 12x Combine like terms: -15 + 14 = -1 -9 + 10x = -1 + 12x Solving -9 + 10x = -1 + 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. -9 + 10x + -12x = -1 + 12x + -12x Combine like terms: 10x + -12x = -2x -9 + -2x = -1 + 12x + -12x Combine like terms: 12x + -12x = 0 -9 + -2x = -1 + 0 -9 + -2x = -1 Add '9' to each side of the equation. -9 + 9 + -2x = -1 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = -1 + 9 -2x = -1 + 9 Combine like terms: -1 + 9 = 8 -2x = 8 Divide each side by '-2'. x = -4 Simplifying x = -4
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