# Absolute Value as Distance From Zero

A solid understanding of absolute value is vital for success in Precalculus and Calculus.

Read through the following lessons: the first few should be quick-and-easy, but it's important to make sure your foundational concepts are sound.

Be sure to click-click-click the web exercises in each section to check your understanding! The lessons will open in a new tab/window.

- Simplifying Basic Absolute Value Expressions
- Determining the Sign (Positive or Negative) of Absolute Value Expressions
- Solving Simple Absolute Value Sentences
- Solving Sentences Involving ‘Plus or Minus’
- Solving Absolute Value Equations
- Solving Absolute Value Inequalities Involving ‘Less Than’
- Solving Absolute Value Inequalities Involving ‘Greater Than’
- Solving Absolute Value Sentences, All Types

If you're in a hurry, here are the key concepts and a few examples. The web exercises on this page are a duplicate of those in Solving Absolute Value Sentences, All Types.

*the absolute value of*$\,x\,.$

## Examples

*all by itself*on one side of the inequality. Thus, your first job is to

*isolate the absolute value*:

*all by itself*on one side of the inequality. Thus, your first job is to

*isolate the absolute value*:

## Concept Practice

Solve the given absolute value sentence. Write the result in the most conventional way.

For more advanced students, a graph is displayed.

For example, the inequality $\,|2 - 3x| \lt 7\,$ is optionally accompanied by the graph of $\,y = |2 - 3x|\,$ (the left side of the inequality, dashed green) and the graph of $\,y = 7\,$ (the right side of the inequality, solid purple).

In this example, you are finding the values of $\,x\,$ where the green
graph lies below the purple graph.
Click the ‘Show/Hide Graph’ button
if you prefer *not* to see the graph.