Question

Find the value of x.

$\frac{x+2}{x+3}=\frac{4}{5}$

Short answer

The value of x is2 .

Step-by-step solution

Step 1. Given information.

The ratio here given is,

$\frac{x+2}{x+3}=\frac{4}{5}$

Step 2. Concept and Formula Used.

The properties of proportion,

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

The given ratio is$\frac{x+2}{x+3}=\frac{4}{5}$,

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

Then,

$\begin{array}{l}5(x+2)=4(x+3)\\ 5x+10=4x+12\left(\text{Usingdistributiveproperty}\right)\\ 5x-4x=12-10\\ x=2\end{array}$

Therefore, the value of x is 2.