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Simplifying 2(x + -4) + 5(x + 7) = 3(x + -1) + 8(x + 2) Reorder the terms: 2(-4 + x) + 5(x + 7) = 3(x + -1) + 8(x + 2) (-4 * 2 + x * 2) + 5(x + 7) = 3(x + -1) + 8(x + 2) (-8 + 2x) + 5(x + 7) = 3(x + -1) + 8(x + 2) Reorder the terms: -8 + 2x + 5(7 + x) = 3(x + -1) + 8(x + 2) -8 + 2x + (7 * 5 + x * 5) = 3(x + -1) + 8(x + 2) -8 + 2x + (35 + 5x) = 3(x + -1) + 8(x + 2) Reorder the terms: -8 + 35 + 2x + 5x = 3(x + -1) + 8(x + 2) Combine like terms: -8 + 35 = 27 27 + 2x + 5x = 3(x + -1) + 8(x + 2) Combine like terms: 2x + 5x = 7x 27 + 7x = 3(x + -1) + 8(x + 2) Reorder the terms: 27 + 7x = 3(-1 + x) + 8(x + 2) 27 + 7x = (-1 * 3 + x * 3) + 8(x + 2) 27 + 7x = (-3 + 3x) + 8(x + 2) Reorder the terms: 27 + 7x = -3 + 3x + 8(2 + x) 27 + 7x = -3 + 3x + (2 * 8 + x * 8) 27 + 7x = -3 + 3x + (16 + 8x) Reorder the terms: 27 + 7x = -3 + 16 + 3x + 8x Combine like terms: -3 + 16 = 13 27 + 7x = 13 + 3x + 8x Combine like terms: 3x + 8x = 11x 27 + 7x = 13 + 11x Solving 27 + 7x = 13 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. 27 + 7x + -11x = 13 + 11x + -11x Combine like terms: 7x + -11x = -4x 27 + -4x = 13 + 11x + -11x Combine like terms: 11x + -11x = 0 27 + -4x = 13 + 0 27 + -4x = 13 Add '-27' to each side of the equation. 27 + -27 + -4x = 13 + -27 Combine like terms: 27 + -27 = 0 0 + -4x = 13 + -27 -4x = 13 + -27 Combine like terms: 13 + -27 = -14 -4x = -14 Divide each side by '-4'. x = 3.5 Simplifying x = 3.5
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