Question

Solve each equation. Check your solution.

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

Short answer

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

Step-by-step solution

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.