Q. 18 - Intermediate Algebra

Question

In the following exercises, solve each equation.

$\frac{3}{2}{b}^2-7=41$

Step-by-Step Solution

Answer

The solution of the equation is $b=4\sqrt{2},-4\sqrt{2}$

Step 1. Given information

In the given question we have to solve given equation.
$\frac{3}{2}{b}^2-7=41$

Step 2. The given equation is 3 2 b 2 − 7 = 41

Isolate the quadratic term.

Add 7 on both side

$$\begin{gathered} \frac{3}{2}{b}^2-7+7=41+7 \\ \frac{3}{2}{b}^2=48 \end{gathered}$$

Multiply by $\frac{2}{3}$ on both side

$$\begin{gathered} \frac{3}{2}{b}^2\times \frac{2}{3}=48\times \frac{2}{3} \\ {b}^2=16\times 2 \end{gathered}$$

Step 3. Use the Square Root Property.

$b=\pm \sqrt{16\times 2}$

Simplify the radical.

$b=\pm 4\sqrt{2}$

Step 4. Rewrite to show two solutions.

$b=4\sqrt{2} b=-4\sqrt{2}$