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

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Answer 1 · 2017-08-01T09:06:58

$x = 24$ $x= 24$

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

$\frac{2 (x + 6)}{3 (x - 2)} = \frac{10 x}{11 x}$ $(2(x+6)) / (3(x−2)) = (10x)/(11x)$

2) Cancel $x$ $x$

$\frac{2 (x + 6)}{3 (x - 2)} = \frac{10}{11}$ $(2(x+6)) / (3(x−2)) = 10/11$

3) Multiply both sides by $3 (x - 2)$ $3(x−2)$

$2(x+6) = 10/11 * 3(x−2)$

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

$x=24$

How do you solve \frac { 2x + 12} { 3x - 6} = \frac { 10x } { 11x }2x+123x−6=10x11x\frac { 2x + 12} { 3x - 6} = \frac { 10x } { 11x }?