Question

Solve for x if ab ≠ 2c

Answer 1

`x=(b+ax)/(2c-ba)`

Explanation:

When given the following expression, one is asked to solve for (x):

`(2x-a)/(b)=(ax+1)/(c)`

Use cross products to rid the variable in the denominator,

`c(2x-a)=b(ax+1)`

Simplify, distribute, multiply every term in the parenthesis by the term outside of it,

`2xc-ac=bax+b`

Inverse operations, collect all terms with variable (x) on one side of the equation:

`2xc-ac = bax + b\\\\2xc - bax = b + ac`

Factor, remove a like term that exists in both of these expressions,

`x(2c-ba)=b+ax`

Inverse operations,

`x=(b+ax)/(2c-ba)`

Answer 2

`x = (ac + b)/(2c - ab)`

Refer to the attachment for step by step explaination.