abs(x-2)+abs(x+6)=10

Solution for abs(x-2)+abs(x+6)=10 equation:

Simplifying
abs(x + -2) + abs(x + 6) = 10

Reorder the terms:
abs(-2 + x) + abs(x + 6) = 10
(-2 * abs + x * abs) + abs(x + 6) = 10
(-2abs + absx) + abs(x + 6) = 10

Reorder the terms:
-2abs + absx + abs(6 + x) = 10
-2abs + absx + (6 * abs + x * abs) = 10
-2abs + absx + (6abs + absx) = 10

Reorder the terms:
-2abs + 6abs + absx + absx = 10

Combine like terms: -2abs + 6abs = 4abs
4abs + absx + absx = 10

Combine like terms: absx + absx = 2absx
4abs + 2absx = 10

Solving
4abs + 2absx = 10

Solving for variable 'a'.

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

Reorder the terms:
-10 + 4abs + 2absx = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 4abs + 2absx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2abs + absx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2abs + absx)' equal to zero and attempt to solve:

Simplifying
-5 + 2abs + absx = 0

Solving
-5 + 2abs + absx = 0

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

Add '5' to each side of the equation.
-5 + 2abs + 5 + absx = 0 + 5

Reorder the terms:
-5 + 5 + 2abs + absx = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2abs + absx = 0 + 5
2abs + absx = 0 + 5

Combine like terms: 0 + 5 = 5
2abs + absx = 5

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.