Q26. - Algebra 2

Question

Solve the equation and check the solution.

 

$-\frac{2}{3}a=14$

Step-by-Step Solution

Answer

The solution is $a=-21$.

Step 1- Consider the equation.

Consider the equation $-\frac{2}{3}a=14$.

 

Multiply both sides of the equation by 3.

Step 2- Step description.

$\begin{array}{l}-\frac{2}{3}a=14\\ -\frac{2}{3}a\times \left(3\right)=14\times 3\\ -2a=42\end{array}$

Step 3- Step description.

Divide both sides of the equation by $-2$.

 

$\begin{array}{l}-2a=42\\ \frac{-2a}{-2}=\frac{42}{-2}\\ a=-21\end{array}$

 

Therefore, the solution is $a=-21$.

Step 4- Verify the solution.

Substitute $a=-21$ in the equation and simplify as follows:

 

 $\begin{array}{l}-\frac{2}{3}a=14\\ -\frac{2}{3}\left(-21\right)=14\\ -2\left(-7\right)=14\\ 14=14\end{array}$

 

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $a=-21$.