Question

Solve each equation. Check your solution.

$\frac{5v-4}{10}=\frac{4}{5}$

Short answer

The solution of the given equation is $v=\frac{12}{5}$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{5v-4}{10}=\frac{4}{5}$”.

Step 2. Solve the given equation.

Solving,

$\frac{5v-4}{10}=\frac{4}{5}$ (Given equation)

$5\left(5v-4\right)=40$ (Cross-multiply)

$25v-20=40$ (Distributive property)

$25v-20+20=40+20$ (Add 20 to both sides)

$25v=60$ (Simplify)

$\frac{25v}{25}=\frac{60}{25}$ (Divide both sides by 4)

$v=\frac{12}{5}$ (Simplify)

So, $v=\frac{12}{5}$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $v=\frac{12}{5}$in the given equation $\frac{5v-4}{10}=\frac{4}{5}$to get,

$\begin{array}{l}\frac{5\left(\frac{12}{5}\right)-4}{10}=\frac{4}{5}\\ \frac{12-4}{10}=\frac{4}{5}\\ \frac{8}{10}=\frac{4}{5}\\ \frac{4}{5}=\frac{4}{5}\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.