Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

Find the real solutions of the equation:

$\sqrt{2x+3}=2$

Step-by-Step Solution

Answer

The solution of the given equation is 

$x=\frac{1}{2}$

Step 1. Given information

The given information is $\sqrt{2x+3}=2$

Step 2. Squaring both sides

Squaring both sides to the equation, we get:

$$\begin{gathered} {\left(\sqrt{2x+3}\right)}^2=2^2 \\ 2x+3=4 \end{gathered}$$

Step 3. Solving the equation

Solving the equation, we get:

$$\begin{gathered} 2x+3=4 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}$$

Step 4. Verify the solution

Substituting $x=\frac{1}{2}$ in the equation we get:

$$\begin{gathered} \sqrt{2x+3}=2 \\ \sqrt{2\times \frac{1}{2}+3}=2 \\ \sqrt{1+3}=2 \\ \sqrt{4}=2 \\ 2=2 \end{gathered}$$

This is true.

Thus, the solution of the equation is:

$x=\frac{1}{2}$.