Q36. - Algebra 1

Question

Solve each equation. Check your solution.

$-\frac{5}{2}=\frac{3}{4}z+\frac{1}{2}$

Step-by-Step Solution

Answer

The solution of the given equation is $z=-4$.

Step 1. Write the given equation.

The given equation is “$-\frac{5}{2}=\frac{3}{4}z+\frac{1}{2}$”.

Step 2. Solve the given equation.

Solving,

 

$-\frac{5}{2}=\frac{3}{4}z+\frac{1}{2}$  (Given equation)

 

$-\frac{5}{2}-\frac{1}{2}=\frac{3}{4}z+\frac{1}{2}-\frac{1}{2}$  (Subtract $\frac{1}{2}$ from both sides)

 

$-3=\frac{3}{4}z$  (Simplify)

 

$-3\times \frac{4}{3}=\frac{3}{4}z\times \frac{4}{3}$  (Multiply both sides by $\frac{4}{3}$)

 

$-4=z$  (Simplify)

 

$z=-4$  (Write the variable on the left-hand side)

 

So, $z=-4$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $z=-4$ in the given equation $-\frac{5}{2}=\frac{3}{4}z+\frac{1}{2}$ to get,

 

$\begin{array}{l}-\frac{5}{2}=\frac{3}{4}\left(-4\right)+\frac{1}{2}\\ -\frac{5}{2}=3\left(-1\right)+\frac{1}{2}\\ -\frac{5}{2}=-3+\frac{1}{2}\\ -\frac{5}{2}=-\frac{5}{2}\end{array}$

 

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.