Q32. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{2b}{3}+6=24$

Step-by-Step Solution

Answer

The solution of the given equation is $b=27$.

Step 1. Write the given equation.

The given equation is “$\frac{2b}{3}+6=24$”.

Step 2. Solve the given equation.

Solving,

 

$\frac{2b}{3}+6=24$  (Given equation)

 

$\frac{2b}{3}+6-6=24-6$  (Subtract 6 from both sides)

 

$\frac{2b}{3}=18$  (Simplify)

 

$\frac{2b}{3}\times \frac{3}{2}=18\times \frac{3}{2}$  (Multiply both sides by $\frac{3}{2}$)

 

$b=27$  (Simplify)

 

So, $b=27$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $b=27$ in the given equation $\frac{2b}{3}+6=24$ to get,

 

$\begin{array}{l}\frac{2\left(27\right)}{3}+6=24\\ 2\left(9\right)+6=24\\ 18+6=24\\ 24=24\end{array}$

 

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.