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Simplifying 2(3x + 4) + -3x + -2 = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) Reorder the terms: 2(4 + 3x) + -3x + -2 = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) (4 * 2 + 3x * 2) + -3x + -2 = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) (8 + 6x) + -3x + -2 = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) Reorder the terms: 8 + -2 + 6x + -3x = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) Combine like terms: 8 + -2 = 6 6 + 6x + -3x = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) Combine like terms: 6x + -3x = 3x 6 + 3x = 6(2x + -3) + 2(3 + -4x) + 5(2x + -3) Reorder the terms: 6 + 3x = 6(-3 + 2x) + 2(3 + -4x) + 5(2x + -3) 6 + 3x = (-3 * 6 + 2x * 6) + 2(3 + -4x) + 5(2x + -3) 6 + 3x = (-18 + 12x) + 2(3 + -4x) + 5(2x + -3) 6 + 3x = -18 + 12x + (3 * 2 + -4x * 2) + 5(2x + -3) 6 + 3x = -18 + 12x + (6 + -8x) + 5(2x + -3) Reorder the terms: 6 + 3x = -18 + 12x + 6 + -8x + 5(-3 + 2x) 6 + 3x = -18 + 12x + 6 + -8x + (-3 * 5 + 2x * 5) 6 + 3x = -18 + 12x + 6 + -8x + (-15 + 10x) Reorder the terms: 6 + 3x = -18 + 6 + -15 + 12x + -8x + 10x Combine like terms: -18 + 6 = -12 6 + 3x = -12 + -15 + 12x + -8x + 10x Combine like terms: -12 + -15 = -27 6 + 3x = -27 + 12x + -8x + 10x Combine like terms: 12x + -8x = 4x 6 + 3x = -27 + 4x + 10x Combine like terms: 4x + 10x = 14x 6 + 3x = -27 + 14x Solving 6 + 3x = -27 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. 6 + 3x + -14x = -27 + 14x + -14x Combine like terms: 3x + -14x = -11x 6 + -11x = -27 + 14x + -14x Combine like terms: 14x + -14x = 0 6 + -11x = -27 + 0 6 + -11x = -27 Add '-6' to each side of the equation. 6 + -6 + -11x = -27 + -6 Combine like terms: 6 + -6 = 0 0 + -11x = -27 + -6 -11x = -27 + -6 Combine like terms: -27 + -6 = -33 -11x = -33 Divide each side by '-11'. x = 3 Simplifying x = 3
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