Q38. - Algebra 1

Question

Solve each equation. Check your solution.

$-\frac{1}{5}-\frac{4}{9}a=\frac{2}{15}$

Step-by-Step Solution

Answer

The solution of the given equation is $a=-\frac{3}{4}$.

Step 1. Write the given equation.

The given equation is “$-\frac{1}{5}-\frac{4}{9}a=\frac{2}{15}$”.

Step 2. Solve the given equation.

Solving,

 

$-\frac{1}{5}-\frac{4}{9}a=\frac{2}{15}$  (Given equation)

 

$-\frac{1}{5}-\frac{4}{9}a+\frac{1}{5}=\frac{2}{15}+\frac{1}{5}$  (Add $\frac{1}{5}$ to both sides)

 

$-\frac{4}{9}a=\frac{1}{3}$  (Simplify)

 

$-\frac{4}{9}a\times \left(-\frac{9}{4}\right)=\frac{1}{3}\times \left(-\frac{9}{4}\right)$  (Multiply both sides by $-\frac{9}{4}$)

 

$a=-\frac{3}{4}$  (Simplify)

 

So, $a=-\frac{3}{4}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $a=-\frac{3}{4}$ in the given equation $-\frac{1}{5}-\frac{4}{9}a=\frac{2}{15}$ to get,

 

$\begin{array}{l}-\frac{1}{5}-\frac{4}{9}\left(-\frac{3}{4}\right)=\frac{2}{15}\\ -\frac{1}{5}+\frac{1}{3}=\frac{2}{15}\\ \frac{-3+5}{15}=\frac{2}{15}\\ \frac{2}{15}=\frac{2}{15}\end{array}$

 

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.