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Simplifying 3x + 1 + 2(1 + 4x) = 5(1 + -1x) + 4(2x + 1) 3x + 1 + (1 * 2 + 4x * 2) = 5(1 + -1x) + 4(2x + 1) 3x + 1 + (2 + 8x) = 5(1 + -1x) + 4(2x + 1) Reorder the terms: 1 + 2 + 3x + 8x = 5(1 + -1x) + 4(2x + 1) Combine like terms: 1 + 2 = 3 3 + 3x + 8x = 5(1 + -1x) + 4(2x + 1) Combine like terms: 3x + 8x = 11x 3 + 11x = 5(1 + -1x) + 4(2x + 1) 3 + 11x = (1 * 5 + -1x * 5) + 4(2x + 1) 3 + 11x = (5 + -5x) + 4(2x + 1) Reorder the terms: 3 + 11x = 5 + -5x + 4(1 + 2x) 3 + 11x = 5 + -5x + (1 * 4 + 2x * 4) 3 + 11x = 5 + -5x + (4 + 8x) Reorder the terms: 3 + 11x = 5 + 4 + -5x + 8x Combine like terms: 5 + 4 = 9 3 + 11x = 9 + -5x + 8x Combine like terms: -5x + 8x = 3x 3 + 11x = 9 + 3x Solving 3 + 11x = 9 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. 3 + 11x + -3x = 9 + 3x + -3x Combine like terms: 11x + -3x = 8x 3 + 8x = 9 + 3x + -3x Combine like terms: 3x + -3x = 0 3 + 8x = 9 + 0 3 + 8x = 9 Add '-3' to each side of the equation. 3 + -3 + 8x = 9 + -3 Combine like terms: 3 + -3 = 0 0 + 8x = 9 + -3 8x = 9 + -3 Combine like terms: 9 + -3 = 6 8x = 6 Divide each side by '8'. x = 0.75 Simplifying x = 0.75
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