/*! 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 24 Solve each inequality and graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 24

Solve each inequality and graph the solution set on a number line. \(3 x+2 \leq 14\)

Short Answer

Expert verified
The solution to the inequality is \(x \leq 4\), represented by a solid circle at 4 and a line extending to the left on the number line.

Step by step solution

01

Subtract 2 from both sides of the inequality

Subtracting 2 from both sides of the equation provides \(3x \leq 14 - 2\), which simplifies to \(3x \leq 12\).
02

Divide both sides of the inequality by 3

Solving for x by dividing both sides by 3, provides \(x \leq 12 / 3\), which simplifies to \(x \leq 4\).
03

Plot the solution on the number line

Since we have \(x \leq 4\), we plot a solid circle at 4 to include this number in the solution and a line extending to the left, towards negative infinity, as x can take any value less than or equal to 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.

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

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(2 x^{2}+5 x-3\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(6 x^{2}-11 x+4\)

Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

Solve the quadratic equations in Exercises \(37-52\) by factoring. \(x^{2}+8 x+15=0\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.