Question

Find the value of x.

$\frac{7}{6x-4}=\frac{9}{4x+6}$

Short answer

The value of x is3 .

Step-by-step solution

Step 1. Given information.

The ratio here given is,

$\frac{7}{6x-4}=\frac{9}{4x+6}$

Step 2. Concept and Formula Used.

The properties of proportion,

if$\frac{a}{b}=\frac{c}{d}$ then,$ad=bc$

The given ratio is$\frac{7}{6x-4}=\frac{9}{4x+6}$,

Step 3. Use the property of proportion, if ab=cd then,ad=bc .

Then,

$\begin{array}{l}7(4x+6)=9(6x-4)\\ 28x+42=54x-36\left(\text{Usingdistributiveproperty}\right)\\ 28x-54x=-36-42\\ -26x=-78\end{array}$

Step 4. Divide both sides by -26.

$\begin{array}{l}\frac{-26x}{-26}=\frac{-78}{-26}\\ x=3\end{array}$

Therefore, the value of x is 3.