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Simplifying x + -1[(x + -1y) + (y + -1x)] = 0 Remove parenthesis around (x + -1y) x + -1[x + -1y + (y + -1x)] = 0 Reorder the terms: x + -1[x + -1y + (-1x + y)] = 0 Remove parenthesis around (-1x + y) x + -1[x + -1y + -1x + y] = 0 Reorder the terms: x + -1[x + -1x + -1y + y] = 0 Combine like terms: x + -1x = 0 x + -1[0 + -1y + y] = 0 x + -1[-1y + y] = 0 Combine like terms: -1y + y = 0 x + -1[0] = 0 Multiply -1 * 0 x + 0 = 0 Anything times zero is zero. x + 0 = 0 Reorder the terms: 0 + x = 0 Remove the zero: x = 0 Solving x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x = 0
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