Question

Solve:$\frac{2x+15}{9}=\frac{7x+3}{15}$.

Short answer

The value of x is 6.

Step-by-step solution

Step 1. Given Information

We are given with two ratios equal to each other and we need to solve it for x:

$\frac{2x+15}{9}=\frac{7x+3}{15}.$

Step 2. Solving for x

Firstly find LCM of 9 and 15 which is 45

Now, multiply both sides of the equation with this LCM and solving for x:

$$\begin{gathered} 45\left(\frac{2x+15}{9}\right)=45\left(\frac{7x+3}{15}\right), \\ 10x+75=21x+9, \\ (21-10)x=75-9, \\ 11x=66, \\ x=\frac{66}{11}=6. \end{gathered}$$

Step 3. Checking the result

We get $x=6$as our result and now we will check it from the original equation:

$$\begin{gathered} Putx=6in: \\ \frac{2x+15}{9}=\frac{7x+3}{15}, \\ \frac{2\times 6+15}{9}=\frac{7\times 6+3}{15}, \\ \frac{27}{9}=\frac{45}{15}, \\ 3=3. \end{gathered}$$

This means our result is correct.