If you"re teaching math come students that are prepared to learn about absolute value, typically approximately Grade 6, here"s review of the topic, together with two lessons come introduce and develop the principle with your students.

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## What does Absolute value Mean?

Absolute value describes the distance from zero the a number is top top the number line, without considering direction. The absolute value of a number is never negative. Take a watch at part examples.

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

The absolute worth of –5 is 5. The distance 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 units from zero.

The absolute worth of 0 is 0. (This is why we don"t say that the absolute value of a number is positive. Zero is neither negative nor positive.)

## Absolute worth Examples and also Equations

The many common way to stand for the absolute value of a number or expression is come surround it through the absolute worth symbol: two 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 worth of the expression –2 minus x.–|x| means “the negative of the absolute worth of x.

The number line is not just a means to display distance indigenous zero; it"s likewise a useful method to graph equalities and inequalities the contain expressions with absolute value.

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

Now take into consideration |x| > 2. To display x top top the number line, you need to display every number whose absolute value is greater than 2. When you graph this top top a number line, use open up dots at –2 and 2 to show that those numbers space not component of the graph:

In general, you acquire two set of values for any type of inequality |x| > k or |x| ≥ k, wherein k is any type of number.

Now consider |x| ≤ 2. Friend are trying to find numbers whose absolute worths are much less than or equal to 2. This is true for any type of number between 0 and also 2, including both 0 and also 2. It is likewise true for every one of the the contrary numbers between –2 and also 0. As soon as you graph this ~ above a number line, the closeup of the door dots in ~ –2 and 2 show that those numbers room included. This is as result of the inequality using ≤ (less 보다 or same to) instead of

Math activities and Lessons qualities 6-8