(x-6)-(2x-8)=1

Solution for (x-6)-(2x-8)=1 equation:

Simplifying
(x + -6) + -1(2x + -8) = 1

Reorder the terms:
(-6 + x) + -1(2x + -8) = 1

Remove parenthesis around (-6 + x)
-6 + x + -1(2x + -8) = 1

Reorder the terms:
-6 + x + -1(-8 + 2x) = 1
-6 + x + (-8 * -1 + 2x * -1) = 1
-6 + x + (8 + -2x) = 1

Reorder the terms:
-6 + 8 + x + -2x = 1

Combine like terms: -6 + 8 = 2
2 + x + -2x = 1

Combine like terms: x + -2x = -1x
2 + -1x = 1

Solving
2 + -1x = 1

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 1 + -2

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

Combine like terms: 1 + -2 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1