Q4. - Algebra 1

Question

Solve each equation. Check your solutions.

$\frac{2}{3}=w+\frac{1}{4}$

Step-by-Step Solution

Answer

The $w=\frac{5}{12}$ is the solution of the given equation.

Step 1. Given information.

We have an equation $\frac{2}{3}=w+\frac{1}{4}$.

To find the solution of the given equation and check the solution.

Step 2. Calculation.

Solving the given equation:

$\begin{array}{l}\frac{2}{3}=w+\frac{1}{4}\\ \Rightarrow w=\frac{2}{3}-\frac{1}{4}\\ \Rightarrow w=\frac{8-3}{12}\\ \Rightarrow w=\frac{5}{12}\end{array}$

Step 3. Check the Solution.

We substitute the $w=\frac{5}{12}$ in the given equation.

$\begin{array}{l}\frac{2}{3}=w+\frac{1}{4}\\ \Rightarrow \frac{2}{3}=\frac{5}{12}+\frac{1}{4}\\ \Rightarrow \frac{2}{3}=\frac{5+3}{12}\\ \Rightarrow \frac{2}{3}=\frac{8}{12}=\frac{4\times 2}{4\times 3}\\ \Rightarrow \frac{2}{3}=\frac{2}{3}\\ \Rightarrow L.H.S=R.H.S\end{array}$

Hence, the $w=\frac{5}{12}$ is the solution of the given equation.