How Do You Solve an AND Absolute Value Inequality and Graph It On a Number Line?

Note:

Trying to solve an absolute value inequality? No sweat! This tutorial will take you through the process of solving the inequality. Then you'll see how to write the answer in set builder notation and graph it on a number line. You'll see it all in this tutorial!

Keywords:

problem
absolute value
compound
compound inequality
set builder notation
graph
number line
graph on number line
solve
absolute value inequality

Background Tutorials

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
- What's an Inequality?
  
  Inequalities come up all the time when you're working algebra problems. In this tutorial you'll learn what an inequality is, and you'll see all the common inequality symbols that you're likely to see :)
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
- What Does Absolute Value Mean?
  
  In this tutorial you'll see how you can think of absolute value in a very intuitive way. Let us know if you have any questions about it!
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- What is a Variable?
  
  You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
- How Do You Graph an Inequality or an Infinite Set on a Number Line?
  
  Number lines are really useful in visualizing an inequality or a set. In this tutorial, you'll see how to graph both. Take a look!
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
- How Do You Write Inequalities in Set Builder Notation?
  
  Need some extra practice converting solution phrases into set builder notation? This tutorial was made for you! Follow along as this tutorial shows you how to dissect each phrase and turn it into a solution in set builder notation.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- How Do You Solve an AND Compound Inequality and Graph It On a Number Line?
  
  Trying to solve a compound inequality? No sweat! This tutorial will take you through the process of solving the inequality. Then you'll see how to write the answer in set builder notation and graph it on a number line. You'll see it all in this tutorial!
- How Do You Solve and Graph a Two-Step Inequality?
  
  Solving an inequality for a variable? Just perform the order of operations in reverse! Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.
- How Do You Solve an Inequality with Negative Numbers Using Division?
  
  Solving an inequality for a variable? Just perform the order of operations in reverse! Don't forget that if you multiply or divide by a negative number, you M

How Do You Solve an AND Absolute Value Inequality and Graph It On a Number Line?

How Do You Solve an AND Absolute Value Inequality and Graph It On a Number Line?

Note:

Keywords:

What's an Inequality?

What Does Absolute Value Mean?

What is a Variable?

How Do You Graph an Inequality or an Infinite Set on a Number Line?

How Do You Write Inequalities in Set Builder Notation?

How Do You Solve an AND Compound Inequality and Graph It On a Number Line?

How Do You Solve and Graph a Two-Step Inequality?

How Do You Solve an Inequality with Negative Numbers Using Division?

How Do You Use Subtraction to Solve an Inequality Word Problem?

How Do You Use Addition to Solve an Inequality Word Problem?

How Do You Solve a Word Problem Using an AND Absolute Value Inequality?

How Do You Solve an AND Absolute Value Inequality and Graph It On a Number Line?

How Do You Solve an AND Absolute Value Inequality and Graph It On a Number Line?

Note:

Keywords:

Background Tutorials

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Further Exploration

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.