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