Question

Find the value of x.

$\frac{x+4}{x-4}=\frac{6}{5}$

Short answer

The value of x is 44.

Step-by-step solution

Step 1. Given information.

The ratio here given is,

$\frac{x+4}{x-4}=\frac{6}{5}$

Step 2. Concept and Formula Used.

The properties of proportion,

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

The given ratio is$\frac{x+4}{x-4}=\frac{6}{5}$,

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

Then,

$\begin{array}{l}5(x+4)=6(x-4)\\ 5x+20=6x-24\left(\text{Usingdistributiveproperty}\right)\\ 5x-6x=-24-20\\ -x=-44\\ x=44\end{array}$

Therefore, the value of x is 44.