ax+x-1=0

Solution for ax+x-1=0 equation:

Simplifying
ax + x + -1 = 0

Reorder the terms:
-1 + ax + x = 0

Solving
-1 + ax + x = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + ax + 1 + x = 0 + 1

Reorder the terms:
-1 + 1 + ax + x = 0 + 1

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

Combine like terms: 0 + 1 = 1
ax + x = 1

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

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

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

Simplifying
a = x-1 + -1

Reorder the terms:
a = -1 + x-1