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

Aug 1, 2017

$x = 24$

#### 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 $\frac{30 \left(x - 2\right)}{11}$

$2 \left(x + 6\right) = \frac{30 \left(x - 2\right)}{11}$

5) Multiply both sides by $11$

22(x+6)=30(x−2)

6) Expand

22x+132=30x−60

7) Subtract $22 x$ from both sides

132=30x−60−22x

8) Simplify 30x−60−22x to 8x−60

132=8x−60

9) Add $60$ to both sides

$192 = 8 x$

10) Divide both sides by $8$

$24 = x$

11) Switch sides

$x = 24$