Question

Find the value of x.

$\frac{2x+1}{4x-1}=\frac{2}{3}$

Short answer

The value of x is$\frac{5}{2}$ .

Step-by-step solution

Step 1. Given information.

The ratio here given is,

$\frac{2x+1}{4x-1}=\frac{2}{3}$

Step 2. Concept and Formula Used.

The properties of proportion,

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

The given ratio is$\frac{2x+1}{4x-1}=\frac{2}{3}$,

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

Then,

$\begin{array}{l}3(2x+1)=2(4x-1)\\ 6x+3=8x-2\left(\text{Usingdistributiveproperty}\right)\\ 6x-8x=-2-3\\ -2x=-5\end{array}$

Step 4. Divide both sides by -2.

$\begin{array}{l}\frac{-2x}{-2}=\frac{-5}{-2}\\ x=\frac{5}{2}\end{array}$

Therefore, the value of x is $\frac{5}{2}$.