Q34. - Algebra 1

Question

Solve each equation. Check your solution.

$65=\frac{3}{4}c-7$

Step-by-Step Solution

Answer

The solution of the given equation is $c=96$.

Step 1. Write the given equation.

The given equation is “$65=\frac{3}{4}c-7$”.

Step 2. Solve the given equation.

Solving,

 

$65=\frac{3}{4}c-7$  (Given equation)

 

$65+7=\frac{3}{4}c-7+7$  (Add 7 to both sides)

 

$72=\frac{3}{4}c$  (Simplify)

 

$72\times \frac{4}{3}=\frac{3}{4}c\times \frac{4}{3}$  (Multiply both sides by $\frac{4}{3}$)

 

$96=c$  (Simplify)

 

$c=96$  (Write the variable on the left-hand side)

 

So, $c=96$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $c=96$ in the given equation $65=\frac{3}{4}c-7$ to get,

 

$\begin{array}{l}65=\frac{3}{4}\left(96\right)-7\\ 65=3\left(24\right)-7\\ 65=72-7\\ 65=65\end{array}$

 

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.