Q17. - Algebra 1

Question

Solve each equation. Check your solution.

$1+\frac{r}{9}=4$

Step-by-Step Solution

Answer

The solution of the given equation is $r=27$.

Step 1. Write the given equation.

The given equation is “$1+\frac{r}{9}=4$”.

Step 2. Solve the given equation.

Solving,

 

$1+\frac{r}{9}=4$  (Given equation)

 

$1+\frac{r}{9}-1=4-1$  (Subtract 1 from both sides)

 

$\frac{r}{9}=3$  (Simplify)

 

$\frac{r}{9}\times 9=3\times 9$  (Multiply both sides by 9)

 

$r=27$  (Simplify)

 

So, $r=27$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $r=27$ in the given equation $1+\frac{r}{9}=4$ to get,

 

$\begin{array}{l}1+\frac{27}{9}=4\\ 1+3=4\\ 4=4\end{array}$

 

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.