Abs(5x-4)=abs(x)+4*abs(x-1)

Solution for Abs(5x-4)=abs(x)+4*abs(x-1) equation:

Simplifying
Abs(5x + -4) = abs(x) + 4abs(x + -1)

Reorder the terms:
bsA(-4 + 5x) = abs(x) + 4abs(x + -1)
(-4 * bsA + 5x * bsA) = abs(x) + 4abs(x + -1)
(-4bsA + 5bsxA) = abs(x) + 4abs(x + -1)

Multiply abs * x
-4bsA + 5bsxA = absx + 4abs(x + -1)

Reorder the terms:
-4bsA + 5bsxA = absx + 4abs(-1 + x)
-4bsA + 5bsxA = absx + (-1 * 4abs + x * 4abs)
-4bsA + 5bsxA = absx + (-4abs + 4absx)

Reorder the terms:
-4bsA + 5bsxA = -4abs + absx + 4absx

Combine like terms: absx + 4absx = 5absx
-4bsA + 5bsxA = -4abs + 5absx

Solving
-4bsA + 5bsxA = -4abs + 5absx

Solving for variable 'b'.

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

Add '4abs' to each side of the equation.
-4bsA + 4abs + 5bsxA = -4abs + 4abs + 5absx

Reorder the terms:
4abs + -4bsA + 5bsxA = -4abs + 4abs + 5absx

Combine like terms: -4abs + 4abs = 0
4abs + -4bsA + 5bsxA = 0 + 5absx
4abs + -4bsA + 5bsxA = 5absx

Add '-5absx' to each side of the equation.
4abs + -4bsA + -5absx + 5bsxA = 5absx + -5absx

Reorder the terms:
4abs + -5absx + -4bsA + 5bsxA = 5absx + -5absx

Combine like terms: 5absx + -5absx = 0
4abs + -5absx + -4bsA + 5bsxA = 0

Factor out the Greatest Common Factor (GCF), 'bs'.
bs(4a + -5ax + -4A + 5xA) = 0

Subproblem 1
Set the factor 'bs' equal to zero and attempt to solve:

Simplifying
bs = 0

Solving
bs = 0

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

Simplifying
bs = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4a + -5ax + -4A + 5xA)' equal to zero and attempt to solve:

Simplifying
4a + -5ax + -4A + 5xA = 0

Reorder the terms:
-4A + 4a + -5ax + 5xA = 0

Solving
-4A + 4a + -5ax + 5xA = 0

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

Add '4A' to each side of the equation.
-4A + 4a + -5ax + 4A + 5xA = 0 + 4A

Reorder the terms:
-4A + 4A + 4a + -5ax + 5xA = 0 + 4A

Combine like terms: -4A + 4A = 0
0 + 4a + -5ax + 5xA = 0 + 4A
4a + -5ax + 5xA = 0 + 4A
Remove the zero:
4a + -5ax + 5xA = 4A

Add '-4a' to each side of the equation.
4a + -5ax + -4a + 5xA = 4A + -4a

Reorder the terms:
4a + -4a + -5ax + 5xA = 4A + -4a

Combine like terms: 4a + -4a = 0
0 + -5ax + 5xA = 4A + -4a
-5ax + 5xA = 4A + -4a

Add '5ax' to each side of the equation.
-5ax + 5ax + 5xA = 4A + -4a + 5ax

Combine like terms: -5ax + 5ax = 0
0 + 5xA = 4A + -4a + 5ax
5xA = 4A + -4a + 5ax

Add '-5xA' to each side of the equation.
5xA + -5xA = 4A + -4a + 5ax + -5xA

Combine like terms: 5xA + -5xA = 0
0 = 4A + -4a + 5ax + -5xA

Simplifying
0 = 4A + -4a + 5ax + -5xA

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.