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Simplifying abs(x + -2) + abs(2x + -1) = abs(x + 3) + x + -1 Reorder the terms: abs(-2 + x) + abs(2x + -1) = abs(x + 3) + x + -1 (-2 * abs + x * abs) + abs(2x + -1) = abs(x + 3) + x + -1 (-2abs + absx) + abs(2x + -1) = abs(x + 3) + x + -1 Reorder the terms: -2abs + absx + abs(-1 + 2x) = abs(x + 3) + x + -1 -2abs + absx + (-1 * abs + 2x * abs) = abs(x + 3) + x + -1 -2abs + absx + (-1abs + 2absx) = abs(x + 3) + x + -1 Reorder the terms: -2abs + -1abs + absx + 2absx = abs(x + 3) + x + -1 Combine like terms: -2abs + -1abs = -3abs -3abs + absx + 2absx = abs(x + 3) + x + -1 Combine like terms: absx + 2absx = 3absx -3abs + 3absx = abs(x + 3) + x + -1 Reorder the terms: -3abs + 3absx = abs(3 + x) + x + -1 -3abs + 3absx = (3 * abs + x * abs) + x + -1 -3abs + 3absx = (3abs + absx) + x + -1 Reorder the terms: -3abs + 3absx = -1 + 3abs + absx + x Solving -3abs + 3absx = -1 + 3abs + absx + x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3abs' to each side of the equation. -3abs + -3abs + 3absx = -1 + 3abs + absx + -3abs + x Combine like terms: -3abs + -3abs = -6abs -6abs + 3absx = -1 + 3abs + absx + -3abs + x Reorder the terms: -6abs + 3absx = -1 + 3abs + -3abs + absx + x Combine like terms: 3abs + -3abs = 0 -6abs + 3absx = -1 + 0 + absx + x -6abs + 3absx = -1 + absx + x Add '-1absx' to each side of the equation. -6abs + 3absx + -1absx = -1 + absx + -1absx + x Combine like terms: 3absx + -1absx = 2absx -6abs + 2absx = -1 + absx + -1absx + x Combine like terms: absx + -1absx = 0 -6abs + 2absx = -1 + 0 + x -6abs + 2absx = -1 + x Reorder the terms: 1 + -6abs + 2absx + -1x = -1 + x + 1 + -1x Reorder the terms: 1 + -6abs + 2absx + -1x = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 1 + -6abs + 2absx + -1x = 0 + x + -1x 1 + -6abs + 2absx + -1x = x + -1x Combine like terms: x + -1x = 0 1 + -6abs + 2absx + -1x = 0 The solution to this equation could not be determined.
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