Chapter 1.3, Problem 33AYU

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

$\sqrt{x+1}=4$

To determine

To find: The solution for the equation $\sqrt{x+1} = 4$ algebraically and verify using a graphing utility.

Answer to Problem 33AYU

Solution:

$x\text{ = 15}$

Explanation of Solution

Given:

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

Algebraic solution:

$\sqrt{x+1} = 4$

$x\text{ + 1 = 16}$Square both sides

$x\text{ + 1 − 1 = 16 − 1}$Subtract 1 from both sides

$x\text{ = 15 }$

Check:

Let $x\text{ = 15}$ in the expression in $x$ on the left side of the equation

$\sqrt{x+1} = \sqrt{15+1}$

$= \sqrt{16}$

$\text{= 4}$

Since the expression on the left side give 4 which is on the right side, the solution $x\text{ = 15}$ checks.