Question

In the following exercises, solve.

$\frac{5}{3v-2}=\frac{7}{4v}$

Short answer

The solution of the equation $\frac{5}{3v-2}=\frac{7}{4v}$is

$v=14$

Step-by-step solution

Step 1. Given information  

The given equation is

$\frac{5}{3v-2}=\frac{7}{4v}$

Step 2. Solution of equation  

Terms of the equation are not defined for the$v=\frac{2}{3}\&v=0$

sorole="math" localid="1647800893161" $\frac{5}{3v-2}=\frac{7}{4v},v\ne \frac{2}{3},v\ne 0$

The least common denominator of all denominators in the equation is$4v(3v-2)$

multiply both sides of the equation by the least common denominator $4v(3v-2)$

$$\begin{gathered} 4v(3v-2)\left(\frac{5}{3v-2}\right)=4v(3v-2)\left(\frac{7}{4v}\right) \\ 4v\left(5\right)=(3v-2)\left(7\right) \\ 20v=21v-14 \\ v=14 \end{gathered}$$

So the solution of the equation is $v=14$

Step 3. Verification 

Substitute $v=14$in the equation

$$\begin{gathered} \frac{5}{3v-2}=\frac{7}{4v} \\ \frac{5}{3\left(14\right)-2}\stackrel{?}{=}\frac{7}{4\left(14\right)} \\ \frac{5}{42-2}\stackrel{?}{=}\frac{7}{56} \\ \frac{5}{40}\stackrel{?}{=}\frac{7}{56} \\ \frac{1}{8}=\frac{1}{8} \end{gathered}$$

The left-hand side is equal to the right-hand side so the solution is correct.