abs(x+4)+abs(x-7)=abs(2x-1)

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Solution for abs(x+4)+abs(x-7)=abs(2x-1) equation:


Simplifying
abs(x + 4) + abs(x + -7) = abs(2x + -1)

Reorder the terms:
abs(4 + x) + abs(x + -7) = abs(2x + -1)
(4 * abs + x * abs) + abs(x + -7) = abs(2x + -1)
(4abs + absx) + abs(x + -7) = abs(2x + -1)

Reorder the terms:
4abs + absx + abs(-7 + x) = abs(2x + -1)
4abs + absx + (-7 * abs + x * abs) = abs(2x + -1)
4abs + absx + (-7abs + absx) = abs(2x + -1)

Reorder the terms:
4abs + -7abs + absx + absx = abs(2x + -1)

Combine like terms: 4abs + -7abs = -3abs
-3abs + absx + absx = abs(2x + -1)

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

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

Add '-2absx' to each side of the equation.
-3abs + 2absx + -2absx = -1abs + 2absx + -2absx

Combine like terms: 2absx + -2absx = 0
-3abs + 0 = -1abs + 2absx + -2absx
-3abs = -1abs + 2absx + -2absx

Combine like terms: 2absx + -2absx = 0
-3abs = -1abs + 0
-3abs = -1abs

Solving
-3abs = -1abs

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'abs' to each side of the equation.
-3abs + abs = -1abs + abs

Combine like terms: -3abs + abs = -2abs
-2abs = -1abs + abs

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

Divide each side by '-2'.
abs = 0

Simplifying
abs = 0

The solution to this equation could not be determined.

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