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Simplifying 4(3x + 1) = 7(x + 4) + -2(x + 5) Reorder the terms: 4(1 + 3x) = 7(x + 4) + -2(x + 5) (1 * 4 + 3x * 4) = 7(x + 4) + -2(x + 5) (4 + 12x) = 7(x + 4) + -2(x + 5) Reorder the terms: 4 + 12x = 7(4 + x) + -2(x + 5) 4 + 12x = (4 * 7 + x * 7) + -2(x + 5) 4 + 12x = (28 + 7x) + -2(x + 5) Reorder the terms: 4 + 12x = 28 + 7x + -2(5 + x) 4 + 12x = 28 + 7x + (5 * -2 + x * -2) 4 + 12x = 28 + 7x + (-10 + -2x) Reorder the terms: 4 + 12x = 28 + -10 + 7x + -2x Combine like terms: 28 + -10 = 18 4 + 12x = 18 + 7x + -2x Combine like terms: 7x + -2x = 5x 4 + 12x = 18 + 5x Solving 4 + 12x = 18 + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. 4 + 12x + -5x = 18 + 5x + -5x Combine like terms: 12x + -5x = 7x 4 + 7x = 18 + 5x + -5x Combine like terms: 5x + -5x = 0 4 + 7x = 18 + 0 4 + 7x = 18 Add '-4' to each side of the equation. 4 + -4 + 7x = 18 + -4 Combine like terms: 4 + -4 = 0 0 + 7x = 18 + -4 7x = 18 + -4 Combine like terms: 18 + -4 = 14 7x = 14 Divide each side by '7'. x = 2 Simplifying x = 2
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