Q39. - Algebra 1

Question

Solve each equation. Check your solution.

$-\frac{3}{7}=\frac{3}{4}-\frac{b}{2}$

Step-by-Step Solution

Answer

The solution of the given equation is $b=\frac{33}{14}$.

Step 1. Write the given equation.

The given equation is “$-\frac{3}{7}=\frac{3}{4}-\frac{b}{2}$”.

Step 2. Solve the given equation.

Solving,

 

$-\frac{3}{7}=\frac{3}{4}-\frac{b}{2}$  (Given equation)

 

$-\frac{3}{7}-\frac{3}{4}=\frac{3}{4}-\frac{b}{2}-\frac{3}{4}$  (Subtract $\frac{3}{4}$ from both sides)

 

$-\frac{33}{28}=-\frac{b}{2}$  (Simplify)

 

$-\frac{33}{28}\times \left(-2\right)=-\frac{b}{2}\times \left(-2\right)$  (Multiply both sides by $-2$)

 

$\frac{33}{14}=b$  (Simplify)

 

$b=\frac{33}{14}$  (Write the variable on the left-hand side)

 

So, $b=\frac{33}{14}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $b=\frac{33}{14}$ in the given equation $-\frac{3}{7}=\frac{3}{4}-\frac{b}{2}$ to get,

 

$\begin{array}{l}-\frac{3}{7}=\frac{3}{4}-\frac{1}{2}\left(\frac{33}{14}\right)\\ -\frac{3}{7}=\frac{3}{4}-\frac{33}{28}\\ -\frac{3}{7}=\frac{21-33}{28}\\ -\frac{3}{7}=\frac{-12}{28}\\ -\frac{3}{7}=-\frac{3}{7}\end{array}$

 

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.