Q14. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{b-4}{6}=\frac{b}{2}$

Step-by-Step Solution

Answer

The solution of the given equation is $b=-2$.

Step 1. Write the given equation.

The given equation is “$\frac{b-4}{6}=\frac{b}{2}$”.

Step 2. Solve the given equation.

Solving,

$\frac{b-4}{6}=\frac{b}{2}$  (Given equation)

$2\left(b-4\right)=6b$  (Cross-multiply)

$2b-8=6b$  (Distributive property)

$2b-8-2b=6b-2b$  (Subtract $2b$ from both sides)

$-8=4b$  (Simplify)

$\frac{-8}{4}=\frac{4b}{4}$  (Divide both sides by 4)

$-2=b$  (Simplify)

$b=-2$  (Write the variable on the left-hand side)

So, $b=-2$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $b=-2$ in the given equation $\frac{b-4}{6}=\frac{b}{2}$ to get,

$\begin{array}{l}\frac{-2-4}{6}=\frac{-2}{2}\\ \frac{-6}{6}=-1\\ -1=-1\end{array}$

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.