/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Solve the inequality. Then graph... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 15

Solve the inequality. Then graph the solution set. $$(x+2)^{2} \leq 25$$

Short Answer

Expert verified
The solution to the inequality is \( -7 \leq x \leq 3 \), and the graph shows the range from \( -7 \) to \( 3 \) on a number line.

Step by step solution

01

Remove the Square

The first step is to remove the \( (x + 2)^{2} \). This can be done by taking the square root of both sides. Remember we get two solutions, \(-5\) and \(5\). This simplifies the inequality to \( -5 \leq x + 2 \leq 5 \).
02

Solve for x

Next, isolate the variable \( x \). You subtract 2 from each part of the inequality. This leads to \( -5 - 2 \leq x \leq 5 -2 \), which simplifies to \( -7 \leq x \leq 3 \).
03

Graph

Finally, graph the solution. You create a number line that includes the values from -7 to 3 and all numbers in between. The graph shows the values of \( x \) that satisfy the inequality.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie?

Prove that the complex conjugate of the product of two complex numbers \(a_{1}+b_{1} i\) and \(a_{2}+b_{2} i\) is the product of their complex conjugates.

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=4 x^{2}-8 x+3$$

Decide whether the statement is true or false. Justify your answer. If \(x=-i\) is a zero of the function \(f(x)=x^{3}+i x^{2}+i x-1\) then \(x=i\) must also be a zero of \(f\)

Write the polynomial as the product of linear factors and list all the zeros of the function. $$g(x)=x^{3}-3 x^{2}+x+5$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.