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Simplifying 2(x + 3) = 5(x + -1) + -7(x + -3) + 2 Reorder the terms: 2(3 + x) = 5(x + -1) + -7(x + -3) + 2 (3 * 2 + x * 2) = 5(x + -1) + -7(x + -3) + 2 (6 + 2x) = 5(x + -1) + -7(x + -3) + 2 Reorder the terms: 6 + 2x = 5(-1 + x) + -7(x + -3) + 2 6 + 2x = (-1 * 5 + x * 5) + -7(x + -3) + 2 6 + 2x = (-5 + 5x) + -7(x + -3) + 2 Reorder the terms: 6 + 2x = -5 + 5x + -7(-3 + x) + 2 6 + 2x = -5 + 5x + (-3 * -7 + x * -7) + 2 6 + 2x = -5 + 5x + (21 + -7x) + 2 Reorder the terms: 6 + 2x = -5 + 21 + 2 + 5x + -7x Combine like terms: -5 + 21 = 16 6 + 2x = 16 + 2 + 5x + -7x Combine like terms: 16 + 2 = 18 6 + 2x = 18 + 5x + -7x Combine like terms: 5x + -7x = -2x 6 + 2x = 18 + -2x Solving 6 + 2x = 18 + -2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2x' to each side of the equation. 6 + 2x + 2x = 18 + -2x + 2x Combine like terms: 2x + 2x = 4x 6 + 4x = 18 + -2x + 2x Combine like terms: -2x + 2x = 0 6 + 4x = 18 + 0 6 + 4x = 18 Add '-6' to each side of the equation. 6 + -6 + 4x = 18 + -6 Combine like terms: 6 + -6 = 0 0 + 4x = 18 + -6 4x = 18 + -6 Combine like terms: 18 + -6 = 12 4x = 12 Divide each side by '4'. x = 3 Simplifying x = 3
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