ABS(4k+5)=ABS(3k-2)

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Solution for ABS(4k+5)=ABS(3k-2) equation: 


Simplifying
ABS(4k + 5) = ABS(3k + -2)

Reorder the terms:
ABS(5 + 4k) = ABS(3k + -2)
(5 * ABS + 4k * ABS) = ABS(3k + -2)
(5ABS + 4kABS) = ABS(3k + -2)

Reorder the terms:
5ABS + 4kABS = ABS(-2 + 3k)
5ABS + 4kABS = (-2 * ABS + 3k * ABS)
5ABS + 4kABS = (-2ABS + 3kABS)

Solving
5ABS + 4kABS = -2ABS + 3kABS

Solving for variable 'A'.

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

Add '2ABS' to each side of the equation.
5ABS + 2ABS + 4kABS = -2ABS + 2ABS + 3kABS

Combine like terms: 5ABS + 2ABS = 7ABS
7ABS + 4kABS = -2ABS + 2ABS + 3kABS

Combine like terms: -2ABS + 2ABS = 0
7ABS + 4kABS = 0 + 3kABS
7ABS + 4kABS = 3kABS

Add '-3kABS' to each side of the equation.
7ABS + 4kABS + -3kABS = 3kABS + -3kABS

Combine like terms: 4kABS + -3kABS = 1kABS
7ABS + 1kABS = 3kABS + -3kABS

Combine like terms: 3kABS + -3kABS = 0
7ABS + 1kABS = 0

Factor out the Greatest Common Factor (GCF), 'ABS'.
ABS(7 + k) = 0


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

Simplifying
ABS = 0

Solving
ABS = 0

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

Simplifying
ABS = 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 '(7 + k)' equal to zero and attempt to solve:

Simplifying
7 + k = 0

Solving
7 + k = 0

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

Add '-7' to each side of the equation.
7 + -7 + k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + k = 0 + -7
k = 0 + -7

Combine like terms: 0 + -7 = -7
k = -7

Add '-1k' to each side of the equation.
k + -1k = -7 + -1k

Combine like terms: k + -1k = 0
0 = -7 + -1k

Simplifying
0 = -7 + -1k

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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