Chapter 10: Q28. (page 629)

Solve each equation. Check your solution.
$\sqrt{x + 1} + 2 = 4$

Short Answer

Expert verified

The solution of the given equation is $x = 3$ .

Check:

Substitute 3 for x in the given equation $\sqrt{x + 1} + 2 = 4$ .

$\sqrt{x + 1} + 2 = 4 \sqrt{3 + 1} + 2 \underline{\underline{?}} 4 \sqrt{4} + 2 \underline{\underline{?}} 4 2+2 \underline{\underline{?}} 4 4 = 4$

Therefore, $x = 3$ is the solution of the given equation $\sqrt{x + 1} + 2 = 4$ .

Step by step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$\sqrt{x + 1} + 2 = 4 \sqrt{x + 1} = 4 - 2 \sqrt{x + 1} = 2 {(\sqrt{x + 1})}^{2} = 2^{2} (squaringbothsides) x + 1 = 4$

Step 2. Solve the given equation.

The solution of the given equation is:

$x + 1 = 4 x = 4 - 1 x = 3$

Therefore, the solution of the given equation is $x = 3$ .

Step 3. Check the solution.

Substitute 3 for x in the given equation $\sqrt{x + 1} + 2 = 4$ .

$\sqrt{x + 1} + 2 = 4 \sqrt{3 + 1} + 2 \underline{\underline{?}} 4 \sqrt{4} + 2 \underline{\underline{?}} 4 2+2 \underline{\underline{?}} 4 4 = 4$

Therefore, $x = 3$ is the solution of the given equation $\sqrt{x + 1} + 2 = 4$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each equation. Check your solution.
$\sqrt{x + 1} + 2 = 4$

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution.x+1+2=4

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution.
$\sqrt{x + 1} + 2 = 4$