abs(2x-3a)+abs(a+1-x)=abs(x+1)

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Solution for abs(2x-3a)+abs(a+1-x)=abs(x+1) equation:


Simplifying
abs(2x + -3a) + abs(a + 1 + -1x) = abs(x + 1)

Reorder the terms:
abs(-3a + 2x) + abs(a + 1 + -1x) = abs(x + 1)
(-3a * abs + 2x * abs) + abs(a + 1 + -1x) = abs(x + 1)

Reorder the terms:
(2absx + -3a2bs) + abs(a + 1 + -1x) = abs(x + 1)
(2absx + -3a2bs) + abs(a + 1 + -1x) = abs(x + 1)

Reorder the terms:
2absx + -3a2bs + abs(1 + a + -1x) = abs(x + 1)
2absx + -3a2bs + (1 * abs + a * abs + -1x * abs) = abs(x + 1)

Reorder the terms:
2absx + -3a2bs + (1abs + -1absx + a2bs) = abs(x + 1)
2absx + -3a2bs + (1abs + -1absx + a2bs) = abs(x + 1)

Reorder the terms:
1abs + 2absx + -1absx + -3a2bs + a2bs = abs(x + 1)

Combine like terms: 2absx + -1absx = 1absx
1abs + 1absx + -3a2bs + a2bs = abs(x + 1)

Combine like terms: -3a2bs + a2bs = -2a2bs
1abs + 1absx + -2a2bs = abs(x + 1)

Reorder the terms:
1abs + 1absx + -2a2bs = abs(1 + x)
1abs + 1absx + -2a2bs = (1 * abs + x * abs)
1abs + 1absx + -2a2bs = (1abs + absx)

Add '-1abs' to each side of the equation.
1abs + 1absx + -1abs + -2a2bs = 1abs + -1abs + absx

Reorder the terms:
1abs + -1abs + 1absx + -2a2bs = 1abs + -1abs + absx

Combine like terms: 1abs + -1abs = 0
0 + 1absx + -2a2bs = 1abs + -1abs + absx
1absx + -2a2bs = 1abs + -1abs + absx

Combine like terms: 1abs + -1abs = 0
1absx + -2a2bs = 0 + absx
1absx + -2a2bs = absx

Solving
1absx + -2a2bs = absx

Solving for variable 'a'.

Reorder the terms:
1absx + -1absx + -2a2bs = absx + -1absx

Combine like terms: 1absx + -1absx = 0
0 + -2a2bs = absx + -1absx
-2a2bs = absx + -1absx

Combine like terms: absx + -1absx = 0
-2a2bs = 0

Ignore the factor -2.

Subproblem 1

Set the factor 'a2bs' equal to zero and attempt to solve: Simplifying a2bs = 0 Solving a2bs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2bs = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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