Question

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

$\sqrt{x+1}=4$

Short answer

The required solution is $x=15$. The graph of the solution is given below:

Step-by-step solution

Step 1. Given information. 

We have:

$\sqrt{x+1}=4$

Step 2. Solve the equation algebraically.   

The equation is $\sqrt{x+1}=4$.

Square on both sides:

$$\begin{gathered} {\left(\sqrt{x+1}\right)}^2={\left(4\right)}^2 \\ x+1=16 \\ x=16-1 \\ x=15 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.   

The solution of the equation is $x=15$.

Draw the graph of the equation $\sqrt{x+1}=4$using the graphing utility: