Question

Solve ax - by = f for x

Answer 1

For this case we have the following expression:
 $ax - by = f$
 We must clear the value of x in the expression.
 For this, we must follow the following steps:
 1) add by on both sides of the equation:
 $ax - by + by = f + by ax = f + by$
 2) multiply both sides by 1 / a:
 $(1 / a) * ax = (1 / a) f + (1 / a) by x = (1 / a) f + (1 / a) by$
 3) Common factor 1 / a:
 $x = (1 / a) * (f + by)$
 Answer:
 $x = (1 / a) * (f + by)$