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