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Simplifying 8(x + 1) + 2(5 + -3x) = 4(2x + -3) + -3(x + -6) Reorder the terms: 8(1 + x) + 2(5 + -3x) = 4(2x + -3) + -3(x + -6) (1 * 8 + x * 8) + 2(5 + -3x) = 4(2x + -3) + -3(x + -6) (8 + 8x) + 2(5 + -3x) = 4(2x + -3) + -3(x + -6) 8 + 8x + (5 * 2 + -3x * 2) = 4(2x + -3) + -3(x + -6) 8 + 8x + (10 + -6x) = 4(2x + -3) + -3(x + -6) Reorder the terms: 8 + 10 + 8x + -6x = 4(2x + -3) + -3(x + -6) Combine like terms: 8 + 10 = 18 18 + 8x + -6x = 4(2x + -3) + -3(x + -6) Combine like terms: 8x + -6x = 2x 18 + 2x = 4(2x + -3) + -3(x + -6) Reorder the terms: 18 + 2x = 4(-3 + 2x) + -3(x + -6) 18 + 2x = (-3 * 4 + 2x * 4) + -3(x + -6) 18 + 2x = (-12 + 8x) + -3(x + -6) Reorder the terms: 18 + 2x = -12 + 8x + -3(-6 + x) 18 + 2x = -12 + 8x + (-6 * -3 + x * -3) 18 + 2x = -12 + 8x + (18 + -3x) Reorder the terms: 18 + 2x = -12 + 18 + 8x + -3x Combine like terms: -12 + 18 = 6 18 + 2x = 6 + 8x + -3x Combine like terms: 8x + -3x = 5x 18 + 2x = 6 + 5x Solving 18 + 2x = 6 + 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. 18 + 2x + -5x = 6 + 5x + -5x Combine like terms: 2x + -5x = -3x 18 + -3x = 6 + 5x + -5x Combine like terms: 5x + -5x = 0 18 + -3x = 6 + 0 18 + -3x = 6 Add '-18' to each side of the equation. 18 + -18 + -3x = 6 + -18 Combine like terms: 18 + -18 = 0 0 + -3x = 6 + -18 -3x = 6 + -18 Combine like terms: 6 + -18 = -12 -3x = -12 Divide each side by '-3'. x = 4 Simplifying x = 4
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