If you\"re teaching math come students who are all set to learn about absolute value, typically roughly Grade 6, here\"s an overview of the topic, together with two lessons come introduce and also develop the principle with your students.

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## What walk Absolute value Mean?

Absolute value explains the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative. Take a look at at part examples.

The absolute worth of 5 is 5. The street from 5 to 0 is 5 units.

The absolute value of –5 is 5. The street from –5 come 0 is 5 units.

The absolute value of 2 + (–7) is 5. Once representing the amount on a number line, the resulting allude is 5 devices from zero.

The absolute worth of 0 is 0. (This is why us don\"t say the the absolute value of a number is positive. Zero is neither an unfavorable nor positive.)

## Absolute worth Examples and Equations

The many common method to represent the absolute worth of a number or expression is come surround it with the absolute worth symbol: 2 vertical straight lines.

|6| = 6 means “the absolute worth of 6 is 6.”|–6| = 6 means “the absolute worth of –6 is 6.|–2 – x| means “the absolute value of the expression –2 minus x.–|x| means “the an adverse of the absolute value of x.

The number heat is not just a means to present distance from zero; it\"s additionally a useful means to graph equalities and inequalities the contain expressions v absolute value.

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Consider the equation |x| = 2. To show x ~ above the number line, you require to present every number who absolute worth is 2. Over there are precisely two places where the happens: in ~ 2 and also at –2:

Now consider |x| > 2. To present x ~ above the number line, you require to display every number who absolute worth is better than 2. Once you graph this top top a number line, use open dots in ~ –2 and 2 to show that those numbers room not part of the graph:

In general, you get two sets of worths for any kind of inequality |x| > k or |x| ≥ k, where k is any kind of number.

Now consider |x| ≤ 2. Friend are looking for numbers who absolute values are much less than or equal to 2. This is true for any kind of number between 0 and also 2, consisting of both 0 and 2. That is likewise true for every one of the the contrary numbers in between –2 and 0. As soon as you graph this top top a number line, the closed dots in ~ –2 and 2 indicate that those numbers space included. This is because of the inequality using ≤ (less than or same to) rather of