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Simplifying 3(x + -2) + 4(2x + -6) = 6(6x + -4) + 8(2x + 1) Reorder the terms: 3(-2 + x) + 4(2x + -6) = 6(6x + -4) + 8(2x + 1) (-2 * 3 + x * 3) + 4(2x + -6) = 6(6x + -4) + 8(2x + 1) (-6 + 3x) + 4(2x + -6) = 6(6x + -4) + 8(2x + 1) Reorder the terms: -6 + 3x + 4(-6 + 2x) = 6(6x + -4) + 8(2x + 1) -6 + 3x + (-6 * 4 + 2x * 4) = 6(6x + -4) + 8(2x + 1) -6 + 3x + (-24 + 8x) = 6(6x + -4) + 8(2x + 1) Reorder the terms: -6 + -24 + 3x + 8x = 6(6x + -4) + 8(2x + 1) Combine like terms: -6 + -24 = -30 -30 + 3x + 8x = 6(6x + -4) + 8(2x + 1) Combine like terms: 3x + 8x = 11x -30 + 11x = 6(6x + -4) + 8(2x + 1) Reorder the terms: -30 + 11x = 6(-4 + 6x) + 8(2x + 1) -30 + 11x = (-4 * 6 + 6x * 6) + 8(2x + 1) -30 + 11x = (-24 + 36x) + 8(2x + 1) Reorder the terms: -30 + 11x = -24 + 36x + 8(1 + 2x) -30 + 11x = -24 + 36x + (1 * 8 + 2x * 8) -30 + 11x = -24 + 36x + (8 + 16x) Reorder the terms: -30 + 11x = -24 + 8 + 36x + 16x Combine like terms: -24 + 8 = -16 -30 + 11x = -16 + 36x + 16x Combine like terms: 36x + 16x = 52x -30 + 11x = -16 + 52x Solving -30 + 11x = -16 + 52x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52x' to each side of the equation. -30 + 11x + -52x = -16 + 52x + -52x Combine like terms: 11x + -52x = -41x -30 + -41x = -16 + 52x + -52x Combine like terms: 52x + -52x = 0 -30 + -41x = -16 + 0 -30 + -41x = -16 Add '30' to each side of the equation. -30 + 30 + -41x = -16 + 30 Combine like terms: -30 + 30 = 0 0 + -41x = -16 + 30 -41x = -16 + 30 Combine like terms: -16 + 30 = 14 -41x = 14 Divide each side by '-41'. x = -0.3414634146 Simplifying x = -0.3414634146
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