Q41. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{2}{3}+r=-\frac{4}{9}$

Step-by-Step Solution

Answer

The required solution is $r=\frac{-10}{9}$.

Step 1. Write the given information.

The given equation is: $\frac{2}{3}+r=-\frac{4}{9}$

Step 2. Calculation.

Consider the given equation,

$$\begin{gathered} \frac{2}{3}+r=-\frac{4}{9} \\ r=-\frac{4}{9}-\frac{2}{3} \\ r=\frac{-4-6}{9} \\ r=\frac{-10}{9} \end{gathered}$$

Step 3. Checking solution.

Substitute $r=\frac{-10}{9}$ in the given equation, we get

$$\begin{gathered} \frac{2}{3}+r=-\frac{4}{9} \\ \frac{2}{3}+\left(-\frac{10}{9}\right)=-\frac{4}{9} \\ \frac{2}{3}-\frac{10}{9}=-\frac{4}{9} \\ \frac{6-10}{9}=-\frac{4}{9} \\ -\frac{4}{9}=-\frac{4}{9} \end{gathered}$$

Hence, proved.