/*! 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 51 Solve each inequality and graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 51

Solve each inequality and graph the solution set on a number line. \(3(x+1)-5<2 x+1\)

Short Answer

Expert verified
The solution set to the inequality is \(x<3\), graphed on a number line as an arrow starting from 3 and pointing to the left. The solution as an interval is \((-鈭�, 3)\).

Step by step solution

01

Distribute 3 in Term Containing x

Apply the distributive property of multiplication over addition to the term \(3(x+1)\) in the inequality. This gives us: \(3x + 3 - 5 < 2x + 1\).
02

Simplify Both Sides

Simplify the inequality by combining like terms. This gives us: \(3x - 2 < 2x + 1\).
03

Manipulate the inequality to isolate x

Manipulate the inequality by combining 3x and -2x. Subtract 2x from both sides of the inequality for which will result in \(3x - 2x < 1 + 2\) and simplify to get \(x < 3\).
04

Graph the Solution

On a number line, a open circle is put on 3 because x is less than 3 (and not less than or equal to 3). Arrow is placed pointing towards the left to show that x includes all numbers less than 3.
05

Define the Interval

The solution as an interval is \((-鈭�, 3)\). The open parenthesis means that 3 is not included in the solution set.

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. \(x(6 x+13)+6=0\)

Use FOIL to find the products. \((x-5)(x+3)\)

Solve the equations using the quadratic formula. \(3 x^{2}=5 x-1\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+17 x+16\)

A car can be rented from Basic Rental for \(\$ 260\) per week with no extra charge for mileage. Continental charges \(\$ 80\) per week plus 25 cents for each mile driven to rent the same car. How many miles must be driven in a week to make the rental cost for Basic Rental a better deal than Continental's?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.