Q41. SGR - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{6r-7}{10}=\frac{r}{4}$

Step-by-Step Solution

Answer

The solution of the equation is $r=2$.

Step 1. Apply the concept of multiplication and division of equality.

We can multiply or divide by same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

We have the equation $\frac{6r-7}{10}=\frac{r}{4}$, we multiply by $10$ both sides of the equation as shown:

$\begin{array}{l}\frac{6r-7}{10}\times 10=\frac{r}{4}\times 10\\ 6r-7=2.5r\end{array}$

Step 2. Apply the concept of addition and subtraction of equality.

We can add or subtract same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

We are given the equation $6r-7=2.5r$, we add 7 to both sides of the equation as shown:

$\begin{array}{l}6r-7+7=2.5r+7\\ 6r=2.5r+7\end{array}$

We are given the equation $6r=2.5r+7$, we add $-2.5r$ to both sides of the equation as shown:

$\begin{array}{l}6r-2.5r=2.5r+7-2.5r\\ 3.5r=7\end{array}$

We have the equation $3.5r=7$, we divide by $3.5$ both sides of the equation as shown:

$\begin{array}{l}\frac{3.5r}{3.5}=\frac{7}{3.5}\\ r=2\end{array}$

 

Thus, the solution of the equation is $r=2$.

Step 3. Checking the solution.

We substitute the value of the variable into the given equation:

$\begin{array}{l}\frac{6r-7}{10}=\frac{r}{4}\\ \frac{6\times 2-7}{10}=\frac{2}{4}\\ \frac{5}{10}=\frac{2}{4}\\ \frac{1}{2}=\frac{1}{2}\end{array}$

Since the above equation is satisfied, the solution $r=2$ is verified.