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

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## What walk Absolute worth Mean?

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

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

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

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

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

## Absolute worth Examples and Equations

The most common method to stand for the absolute worth of a number or expression is come surround it through the absolute worth symbol: 2 vertical directly lines.

|6| = 6 means “the absolute value 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 unfavorable of the absolute value of x.

The number line is not just a way to present distance from zero; it"s also a useful means to graph equalities and also inequalities that contain expressions with absolute value.

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Consider the equation |x| = 2. To display x ~ above the number line, you require to present every number who absolute worth is 2. There are exactly two areas where that happens: at 2 and at –2:

Now take into consideration |x| > 2. To show x ~ above the number line, you require to display every number who absolute worth is better than 2. Once you graph this on a number line, use open up dots at –2 and also 2 to indicate that those numbers room not component of the graph:

In general, you obtain two to adjust of worths for any inequality |x| > k or |x| ≥ k, where k is any number.

Now think about |x| ≤ 2. Friend are searching for numbers whose absolute values are less than or equal to 2. This is true for any kind of number in between 0 and also 2, consisting of both 0 and 2. That is additionally true for every one of the the contrary numbers between –2 and 0. Once you graph this ~ above a number line, the close up door dots in ~ –2 and 2 suggest that those numbers are included. This is due to the inequality utilizing ≤ (less than or same to) instead of

Math tasks and Lessons qualities 6-8