Question

Solve each equation. Check your solution.

$\frac{5}{8}+\frac{3}{4}x=\frac{1}{16}$

Short answer

The required answer is $-\frac{3}{4}$.

Step-by-step solution

Step 1- Isolate the variable x

Perform subtraction of $\frac{5}{8}$on both sides of the equation.

$\begin{array}{c}\frac{5}{8}+\frac{3}{4}x-\frac{5}{8}=\frac{1}{16}-\frac{5}{8}\\ \frac{3}{4}x=-\frac{9}{16}\end{array}$

Perform division of $\frac{3}{4}$on both sides of the equation.

$\begin{array}{c}\frac{\frac{3}{4}x}{\frac{3}{4}}=\frac{-\frac{9}{16}}{\frac{3}{4}}\\ x=-\frac{3}{4}\end{array}$

– Check the obtained value 

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

$\begin{array}{l}\frac{5}{8}+\frac{3}{4}\left(-\frac{3}{4}\right)\stackrel{?}{=}\frac{1}{16}\\ \frac{5}{8}-\frac{9}{16}\stackrel{?}{=}\frac{1}{16}\\ \frac{1}{16}=\frac{1}{16}\end{array}$

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.