Question

How do you solve `\frac{10+4x}{27}+\frac{1-x}{2}-\frac{21x-14}{18}=\frac{2-x}{2}`?

Answer 1

`x = 7/11`

Explanation:

The first thing you could do is eliminate the fractions, by multiplying all terms by the least common multiple of the denominators (which will be `54`). We're then left with

`2(10+4x) + 27(1-x) - 3(21x-14) = 27(2-x)`

Distribute:

`8x + 20 - 27x + 27 - 63x + 42 = -27x + 54`

Isolate the `x`-terms to one side:

`55x = 35`

`x = color(blue)(7/11`