Question

Solve each equation. Check your solution.

$\frac{2}{5}x+\frac{3}{7}=1-\frac{4}{7}x$

Short answer

The required answer is $\frac{10}{17}$.

Step-by-step solution

Step 1- Isolate the variable x

Perform addition of $\frac{4}{7}x$ and subtraction of $\frac{3}{7}$on both the sides of the equation.

$\begin{array}{c}\frac{2}{5}x+\frac{3}{7}+\frac{4}{7}x-\frac{3}{7}=1-\frac{4}{7}x+\frac{4}{7}x-\frac{3}{7}\\ \frac{34}{35}x=\frac{4}{7}\end{array}$

Perform division of $\frac{34}{35}$ on both the sides of the equation

$\begin{array}{c}\frac{\frac{34}{35}x}{\frac{34}{35}}=\frac{\frac{4}{7}}{\frac{34}{35}}\\ x=\frac{10}{17}\end{array}$

– Check the obtained value 

Substitute the obtained value of x into the original equation and perform simplification for checking.

$\begin{array}{l}\frac{2}{5}\left(\frac{10}{17}\right)+\frac{3}{7}\stackrel{?}{=}1-\frac{4}{7}\left(\frac{10}{17}\right)\\ \frac{4}{17}+\frac{3}{7}\stackrel{?}{=}1-\frac{40}{119}\\ \frac{79}{119}=\frac{79}{119}\end{array}$

Step 3- Make the conclusion

As the checking results in equal values on both the sides on substation of obtained value which means that obtained value is correct.