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Simplifying 12(x + 1) + -4(x + -5) = 3(x + -1) + 4x + 8 Reorder the terms: 12(1 + x) + -4(x + -5) = 3(x + -1) + 4x + 8 (1 * 12 + x * 12) + -4(x + -5) = 3(x + -1) + 4x + 8 (12 + 12x) + -4(x + -5) = 3(x + -1) + 4x + 8 Reorder the terms: 12 + 12x + -4(-5 + x) = 3(x + -1) + 4x + 8 12 + 12x + (-5 * -4 + x * -4) = 3(x + -1) + 4x + 8 12 + 12x + (20 + -4x) = 3(x + -1) + 4x + 8 Reorder the terms: 12 + 20 + 12x + -4x = 3(x + -1) + 4x + 8 Combine like terms: 12 + 20 = 32 32 + 12x + -4x = 3(x + -1) + 4x + 8 Combine like terms: 12x + -4x = 8x 32 + 8x = 3(x + -1) + 4x + 8 Reorder the terms: 32 + 8x = 3(-1 + x) + 4x + 8 32 + 8x = (-1 * 3 + x * 3) + 4x + 8 32 + 8x = (-3 + 3x) + 4x + 8 Reorder the terms: 32 + 8x = -3 + 8 + 3x + 4x Combine like terms: -3 + 8 = 5 32 + 8x = 5 + 3x + 4x Combine like terms: 3x + 4x = 7x 32 + 8x = 5 + 7x Solving 32 + 8x = 5 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 32 + 8x + -7x = 5 + 7x + -7x Combine like terms: 8x + -7x = 1x 32 + 1x = 5 + 7x + -7x Combine like terms: 7x + -7x = 0 32 + 1x = 5 + 0 32 + 1x = 5 Add '-32' to each side of the equation. 32 + -32 + 1x = 5 + -32 Combine like terms: 32 + -32 = 0 0 + 1x = 5 + -32 1x = 5 + -32 Combine like terms: 5 + -32 = -27 1x = -27 Divide each side by '1'. x = -27 Simplifying x = -27
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