Q35. - Algebra 1

Question

Solve each equation. Check your solution.

$9+\frac{2}{3}x=81$

Step-by-Step Solution

Answer

The solution of the given equation is $x=108$.

Step 1. Write the given equation.

The given equation is “$9+\frac{2}{3}x=81$”.

Step 2. Solve the given equation.

Solving,

 

$9+\frac{2}{3}x=81$  (Given equation)

 

$9+\frac{2}{3}x-9=81-9$  (Subtract 9 from both sides)

 

$\frac{2}{3}x=72$  (Simplify)

 

$\frac{2}{3}x\times \frac{3}{2}=72\times \frac{3}{2}$  (Multiply both sides by $\frac{3}{2}$)

 

$x=108$  (Simplify)

 

So, $x=108$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=108$ in the given equation  to get,

 

$\begin{array}{l}9+\frac{2}{3}\left(108\right)=81\\ 9+2\left(36\right)=81\\ 9+72=81\\ 81=81\end{array}$

 

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.