Q45. - Algebra 2

Question

Solve each equation. Check your solution.

$\frac{1}{9}-\frac{2}{3}b=\frac{1}{18}$

Step-by-Step Solution

Answer

The required answer is $\frac{1}{12}$.

Step 1- Isolate the variable b

Perform subtraction of $\frac{1}{9}$ on both sides of the equation.

$\begin{array}{c}\frac{1}{9}-\frac{2}{3}b-\frac{1}{9}=\frac{1}{18}-\frac{1}{9}\\ -\frac{2}{3}b=-\frac{1}{18}\end{array}$

Perform division of $-\frac{2}{3}$ on both sides of the equation.

$\begin{array}{c}\frac{-\frac{2}{3}b}{-\frac{2}{3}}=\frac{-\frac{1}{18}}{-\frac{2}{3}}\\ b=\frac{1}{12}\end{array}$

Step 2 – Check the obtained value

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

$\begin{array}{l}\frac{1}{9}-\frac{2}{3}\left(\frac{1}{12}\right)\stackrel{?}{=}\frac{1}{18}\\ \frac{1}{9}-\frac{2}{36}\stackrel{?}{=}\frac{1}{18}\\ \frac{1}{18}=\frac{1}{18}\end{array}$

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.