/*! 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 43 Solve the inequality and graph i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 43

Solve the inequality and graph its solution. \(-2+x<0\)

Short Answer

Expert verified
The solution to the inequality \(-2 + x < 0\) is \(x < 2\), which can be expressed as \(-\infty < x < 2\). The graph of the solution would be a line on a number line extending leftwards from \(x = 2\), not including the point \(x = 2\).

Step by step solution

01

Rearrange the inequality

To begin, rearrange the inequality so \(x\) is isolated on one side. You can do this by adding 2 to both sides of the inequality \(-2 + x + 2 < 0 + 2\) simplifies to \(x < 2\)
02

Identify the solution for the inequality

The inequality \(x < 2\) holds for all values of \(x\) that are less than 2. So, the solution set can be expressed as \(-\infty < x < 2\).
03

Graph the solution

To graph the solution, draw a number line and mark the point at \(x = 2\). Place an open circle at \(x = 2\) to indicate that 2 is not included in the solution. The line extending to the left from the open circle represents all values less than 2, which constitute the solution to 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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Inequality Solution
Solving inequalities is like solving equations, but instead of asserting equality, inequalities indicate a range of possible solutions. For instance, in our inequality \(-2 + x < 0\), we aim to find all possible values for \(x\) that make the inequality true. The goal is to isolate \(x\). Here, adding 2 to both sides simplifies the expression to \(x < 2\). This reveals the solution set: any \(x\) less than 2 satisfies the inequality.
  • Add or subtract terms on both sides to isolate the variable.
  • Remember: keep the inequality sign the same if using addition or subtraction.
Understanding these basic steps allows you to solve a wide array of inequalities efficiently.
Graphing Inequalities
Once we have the inequality solution, it's helpful to visualize it. Graphing inequalities provides a clear picture of where the solutions lie on a number line. For the solution \(x < 2\), we represent this by drawing a number line and indicating the range of values that satisfy the inequality.
  • Draw a horizontal line to represent all possible values.
  • Identify the point that equals your boundary value, like \(x = 2\) in this instance.
  • Use an open circle at \(x = 2\) because 2 is not included in our solution set.
This visual representation helps in understanding inequalities by clearly indicating the range of possible solutions.
Number Line Representation
A number line is a simple yet effective tool for visualizing expressions and inequalities. When graphing the solution to an inequality such as \(x < 2\), a number line allows you to convey this range easily.
  • Begin by drawing a straight line with numbers placed at regular intervals.
  • Mark the boundary value, i.e., 2, with an open circle.
  • Shade the area to the left of this open circle to indicate that all numbers less than 2 are part of the solution set.
This method not only clarifies the solution but also reinforces the understanding that the endpoint is not included, which is important for correctly interpreting inequalities.

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

Find the slope of the graph of the linear function \(f\). $$f(0)=1, f(4)=-1$$

Is each ordered pair a solution of the inequality? $$0.6 x+0.6 y>2.4 ;(2,2),(3,-3)$$

Use the graph of \(y=\frac{2}{3} x-2\) to solve the inequality \(\frac{2}{3} x-2<0 .\) Explain your reasoning.

Sketch the graph of the inequality. $$\frac{1}{4} x+\frac{1}{2} y<1$$

You put 20 slips of paper in a hat. Eight slips are yellow, five slips are blue, and the rest are red. Without looking, you reach into the hat and choose a slip of paper. What is the probability that the slip of paper is not blue?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Discrete 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.