abs(6x)=abs(8x+1)

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Solution for abs(6x)=abs(8x+1) equation:


Simplifying
abs(6x) = abs(8x + 1)

Remove parenthesis around (6x)
abs * 6x = abs(8x + 1)

Reorder the terms for easier multiplication:
6abs * x = abs(8x + 1)

Multiply abs * x
6absx = abs(8x + 1)

Reorder the terms:
6absx = abs(1 + 8x)
6absx = (1 * abs + 8x * abs)
6absx = (1abs + 8absx)

Solving
6absx = 1abs + 8absx

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.
-1abs + 6absx = 1abs + -1abs + 8absx

Combine like terms: 1abs + -1abs = 0
-1abs + 6absx = 0 + 8absx
-1abs + 6absx = 8absx

Add '-8absx' to each side of the equation.
-1abs + 6absx + -8absx = 8absx + -8absx

Combine like terms: 6absx + -8absx = -2absx
-1abs + -2absx = 8absx + -8absx

Combine like terms: 8absx + -8absx = 0
-1abs + -2absx = 0

Factor out the Greatest Common Factor (GCF), '-1abs'.
-1abs(1 + 2x) = 0

Ignore the factor -1.

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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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