/*! 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 52 Solve each inequality and graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 52

Solve each inequality and graph the solution set on a number line. \(4(x+1)+2 \geq 3 x+6\)

Short Answer

Expert verified
The solution to the exercise is \(x \geq 0\). When graphed on a number line, the set of solutions includes 0 and all positive numbers.

Step by step solution

01

Distribute and Simplify

First, distribute the 4 through the parentheses on the left side of the inequality: \(4 \times x + 4 \times 1 +2 \geq 3 x + 6\). This simplifies to \(4x + 4 + 2 \geq 3x + 6\). Combine the constants on the left side, which gives \(4x + 6 \geq 3x + 6\).
02

Isolate the Variable

To isolate x, subtract \(3x\) from both sides of the equation and simultaneously subtract 6 from both sides of the inequality: \(4x - 3x \geq 3x - 3x + 6-6\). This simplifies to \(x \geq 0\).
03

Graph the Inequality

Finally, to graph the inequality on the number line, place a closed dot on zero (because the inequality includes the equal sign) and shade to the right (because x is greater than or equal to zero).

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

Use the five-step strategy for solving word problems to find the number or numbers described. When a number is decreased by \(20 \%\) of itself, the result is 20 . What is the number?

The volume of blood in a person's body is proportional to body weight. A person who weighs 160 pounds has approximately 5 quarts of blood. Estimate the number of quarts of blood in a person who weighs 200 pounds.

In Exercises 33-36, solve each equation using the zero-product principle. \(x^{2}+8 x+15=0\)

Use FOIL to find the products. \((x-1)(x+2)\)

Solve each equation by the method of your choice. \((x-1)(3 x+2)=-7(x-1)\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.