Question

How do you solve `\frac { 2x + 12} { 3x - 6} = \frac { 10x } { 11x }`?

Answer 1

`x= 24`

Explanation:

1) Factor out the common terms `2` and `3`

`(2(x+6)) / (3(x−2)) = (10x)/(11x)`

2) Cancel `x`

`(2(x+6)) / (3(x−2)) = 10/11`

3) Multiply both sides by `3(x−2)`

`2(x+6) = ​10/11​​ * 3(x−2)`

4) Simplify `10/11 * 3(x−2)` to `(30(x-2))/11`

`2(x+6)=(30(x-2))/11`

5) Multiply both sides by `11`

`22(x+6)=30(x−2)`

6) Expand

`22x+132=30x−60`

7) Subtract `22x` from both sides

`132=30x−60−22x`

8) Simplify `30x−60−22x` to `8x−60`

`132=8x−60`

9) Add `60` to both sides

`192=8x`

10) Divide both sides by `8`

`24=x`

11) Switch sides

`x=24`