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Simplifying 3(x + -2) + 4(2x + -6) = 6(x + 4) + 8(2x + 1) Reorder the terms: 3(-2 + x) + 4(2x + -6) = 6(x + 4) + 8(2x + 1) (-2 * 3 + x * 3) + 4(2x + -6) = 6(x + 4) + 8(2x + 1) (-6 + 3x) + 4(2x + -6) = 6(x + 4) + 8(2x + 1) Reorder the terms: -6 + 3x + 4(-6 + 2x) = 6(x + 4) + 8(2x + 1) -6 + 3x + (-6 * 4 + 2x * 4) = 6(x + 4) + 8(2x + 1) -6 + 3x + (-24 + 8x) = 6(x + 4) + 8(2x + 1) Reorder the terms: -6 + -24 + 3x + 8x = 6(x + 4) + 8(2x + 1) Combine like terms: -6 + -24 = -30 -30 + 3x + 8x = 6(x + 4) + 8(2x + 1) Combine like terms: 3x + 8x = 11x -30 + 11x = 6(x + 4) + 8(2x + 1) Reorder the terms: -30 + 11x = 6(4 + x) + 8(2x + 1) -30 + 11x = (4 * 6 + x * 6) + 8(2x + 1) -30 + 11x = (24 + 6x) + 8(2x + 1) Reorder the terms: -30 + 11x = 24 + 6x + 8(1 + 2x) -30 + 11x = 24 + 6x + (1 * 8 + 2x * 8) -30 + 11x = 24 + 6x + (8 + 16x) Reorder the terms: -30 + 11x = 24 + 8 + 6x + 16x Combine like terms: 24 + 8 = 32 -30 + 11x = 32 + 6x + 16x Combine like terms: 6x + 16x = 22x -30 + 11x = 32 + 22x Solving -30 + 11x = 32 + 22x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22x' to each side of the equation. -30 + 11x + -22x = 32 + 22x + -22x Combine like terms: 11x + -22x = -11x -30 + -11x = 32 + 22x + -22x Combine like terms: 22x + -22x = 0 -30 + -11x = 32 + 0 -30 + -11x = 32 Add '30' to each side of the equation. -30 + 30 + -11x = 32 + 30 Combine like terms: -30 + 30 = 0 0 + -11x = 32 + 30 -11x = 32 + 30 Combine like terms: 32 + 30 = 62 -11x = 62 Divide each side by '-11'. x = -5.636363636 Simplifying x = -5.636363636
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