Q37. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{5}{6}k+\frac{2}{3}=\frac{4}{3}$

Step-by-Step Solution

Answer

The solution of the given equation is $k=\frac{4}{5}$.

Step 1. Write the given equation.

The given equation is “$\frac{5}{6}k+\frac{2}{3}=\frac{4}{3}$”.

Step 2. Solve the given equation.

Solving,

 

$\frac{5}{6}k+\frac{2}{3}=\frac{4}{3}$  (Given equation)

 

$\frac{5}{6}k+\frac{2}{3}-\frac{2}{3}=\frac{4}{3}-\frac{2}{3}$  (Subtract $\frac{2}{3}$ from both sides)

 

$\frac{5}{6}k=\frac{2}{3}$  (Simplify)

 

$\frac{5}{6}k\times \frac{6}{5}=\frac{2}{3}\times \frac{6}{5}$  (Multiply both sides by $\frac{6}{5}$)

 

$k=\frac{4}{5}$  (Simplify)

 

So, $k=\frac{4}{5}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $k=\frac{4}{5}$ in the given equation $\frac{5}{6}k+\frac{2}{3}=\frac{4}{3}$ to get,

 

$\begin{array}{l}\frac{5}{6}\left(\frac{4}{5}\right)+\frac{2}{3}=\frac{4}{3}\\ \frac{2}{3}+\frac{2}{3}=\frac{4}{3}\\ \frac{4}{3}=\frac{4}{3}\end{array}$

 

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.