Q. 34 - Precalculus Enhanced with Graphing Utilities

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 

$\sqrt{x-2}=3$

Step-by-Step Solution

Answer

The required solution is $x=11$ and the graph of the solution is given below:

Step 1. Given information.

We have:

$\sqrt{x-2}=3$

Step 2. Solve the equation algebraically.

The equation is $\sqrt{x-2}=3$.

Square on both sides:

$$\begin{gathered} {\left(\sqrt{x-2}\right)}^2={\left(3\right)}^2 \\ x-2=9 \end{gathered}$$

Add $2$ to both sides:

$$\begin{gathered} x-2+2=9+2 \\ x=11 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=11$.

Draw the graph of the equation $\sqrt{x-2}=3$ using the graphing utility: