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Simplifying 2(3x + -1) + 5(x + 4) = 3(x + 7) + -1(x + -6) Reorder the terms: 2(-1 + 3x) + 5(x + 4) = 3(x + 7) + -1(x + -6) (-1 * 2 + 3x * 2) + 5(x + 4) = 3(x + 7) + -1(x + -6) (-2 + 6x) + 5(x + 4) = 3(x + 7) + -1(x + -6) Reorder the terms: -2 + 6x + 5(4 + x) = 3(x + 7) + -1(x + -6) -2 + 6x + (4 * 5 + x * 5) = 3(x + 7) + -1(x + -6) -2 + 6x + (20 + 5x) = 3(x + 7) + -1(x + -6) Reorder the terms: -2 + 20 + 6x + 5x = 3(x + 7) + -1(x + -6) Combine like terms: -2 + 20 = 18 18 + 6x + 5x = 3(x + 7) + -1(x + -6) Combine like terms: 6x + 5x = 11x 18 + 11x = 3(x + 7) + -1(x + -6) Reorder the terms: 18 + 11x = 3(7 + x) + -1(x + -6) 18 + 11x = (7 * 3 + x * 3) + -1(x + -6) 18 + 11x = (21 + 3x) + -1(x + -6) Reorder the terms: 18 + 11x = 21 + 3x + -1(-6 + x) 18 + 11x = 21 + 3x + (-6 * -1 + x * -1) 18 + 11x = 21 + 3x + (6 + -1x) Reorder the terms: 18 + 11x = 21 + 6 + 3x + -1x Combine like terms: 21 + 6 = 27 18 + 11x = 27 + 3x + -1x Combine like terms: 3x + -1x = 2x 18 + 11x = 27 + 2x Solving 18 + 11x = 27 + 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. 18 + 11x + -2x = 27 + 2x + -2x Combine like terms: 11x + -2x = 9x 18 + 9x = 27 + 2x + -2x Combine like terms: 2x + -2x = 0 18 + 9x = 27 + 0 18 + 9x = 27 Add '-18' to each side of the equation. 18 + -18 + 9x = 27 + -18 Combine like terms: 18 + -18 = 0 0 + 9x = 27 + -18 9x = 27 + -18 Combine like terms: 27 + -18 = 9 9x = 9 Divide each side by '9'. x = 1 Simplifying x = 1
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