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Simplifying 3(2x + 4) + 2(4x + 9) = 7(5 + -4x) + -4(2x + -5) Reorder the terms: 3(4 + 2x) + 2(4x + 9) = 7(5 + -4x) + -4(2x + -5) (4 * 3 + 2x * 3) + 2(4x + 9) = 7(5 + -4x) + -4(2x + -5) (12 + 6x) + 2(4x + 9) = 7(5 + -4x) + -4(2x + -5) Reorder the terms: 12 + 6x + 2(9 + 4x) = 7(5 + -4x) + -4(2x + -5) 12 + 6x + (9 * 2 + 4x * 2) = 7(5 + -4x) + -4(2x + -5) 12 + 6x + (18 + 8x) = 7(5 + -4x) + -4(2x + -5) Reorder the terms: 12 + 18 + 6x + 8x = 7(5 + -4x) + -4(2x + -5) Combine like terms: 12 + 18 = 30 30 + 6x + 8x = 7(5 + -4x) + -4(2x + -5) Combine like terms: 6x + 8x = 14x 30 + 14x = 7(5 + -4x) + -4(2x + -5) 30 + 14x = (5 * 7 + -4x * 7) + -4(2x + -5) 30 + 14x = (35 + -28x) + -4(2x + -5) Reorder the terms: 30 + 14x = 35 + -28x + -4(-5 + 2x) 30 + 14x = 35 + -28x + (-5 * -4 + 2x * -4) 30 + 14x = 35 + -28x + (20 + -8x) Reorder the terms: 30 + 14x = 35 + 20 + -28x + -8x Combine like terms: 35 + 20 = 55 30 + 14x = 55 + -28x + -8x Combine like terms: -28x + -8x = -36x 30 + 14x = 55 + -36x Solving 30 + 14x = 55 + -36x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36x' to each side of the equation. 30 + 14x + 36x = 55 + -36x + 36x Combine like terms: 14x + 36x = 50x 30 + 50x = 55 + -36x + 36x Combine like terms: -36x + 36x = 0 30 + 50x = 55 + 0 30 + 50x = 55 Add '-30' to each side of the equation. 30 + -30 + 50x = 55 + -30 Combine like terms: 30 + -30 = 0 0 + 50x = 55 + -30 50x = 55 + -30 Combine like terms: 55 + -30 = 25 50x = 25 Divide each side by '50'. x = 0.5 Simplifying x = 0.5
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