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Simplifying abs(2x + 3) + -1(x + 4) = abs(1 + -1x) Reorder the terms: abs(3 + 2x) + -1(x + 4) = abs(1 + -1x) (3 * abs + 2x * abs) + -1(x + 4) = abs(1 + -1x) (3abs + 2absx) + -1(x + 4) = abs(1 + -1x) Reorder the terms: 3abs + 2absx + -1(4 + x) = abs(1 + -1x) 3abs + 2absx + (4 * -1 + x * -1) = abs(1 + -1x) 3abs + 2absx + (-4 + -1x) = abs(1 + -1x) Reorder the terms: -4 + 3abs + 2absx + -1x = abs(1 + -1x) -4 + 3abs + 2absx + -1x = (1 * abs + -1x * abs) -4 + 3abs + 2absx + -1x = (1abs + -1absx) Solving -4 + 3abs + 2absx + -1x = 1abs + -1absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1abs' to each side of the equation. -4 + 3abs + 2absx + -1abs + -1x = 1abs + -1abs + -1absx Reorder the terms: -4 + 3abs + -1abs + 2absx + -1x = 1abs + -1abs + -1absx Combine like terms: 3abs + -1abs = 2abs -4 + 2abs + 2absx + -1x = 1abs + -1abs + -1absx Combine like terms: 1abs + -1abs = 0 -4 + 2abs + 2absx + -1x = 0 + -1absx -4 + 2abs + 2absx + -1x = -1absx Add 'absx' to each side of the equation. -4 + 2abs + 2absx + absx + -1x = -1absx + absx Combine like terms: 2absx + absx = 3absx -4 + 2abs + 3absx + -1x = -1absx + absx Combine like terms: -1absx + absx = 0 -4 + 2abs + 3absx + -1x = 0 Add '4' to each side of the equation. -4 + 2abs + 3absx + 4 + -1x = 0 + 4 Reorder the terms: -4 + 4 + 2abs + 3absx + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2abs + 3absx + -1x = 0 + 4 2abs + 3absx + -1x = 0 + 4 Combine like terms: 0 + 4 = 4 2abs + 3absx + -1x = 4 Add 'x' to each side of the equation. 2abs + 3absx + -1x + x = 4 + x Combine like terms: -1x + x = 0 2abs + 3absx + 0 = 4 + x 2abs + 3absx = 4 + x Reorder the terms: -4 + 2abs + 3absx + -1x = 4 + x + -4 + -1x Reorder the terms: -4 + 2abs + 3absx + -1x = 4 + -4 + x + -1x Combine like terms: 4 + -4 = 0 -4 + 2abs + 3absx + -1x = 0 + x + -1x -4 + 2abs + 3absx + -1x = x + -1x Combine like terms: x + -1x = 0 -4 + 2abs + 3absx + -1x = 0 The solution to this equation could not be determined.
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