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

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What go Absolute value Mean?

Absolute value defines the distance native zero the a number is ~ above the number line, without considering direction. The absolute worth of a number is never negative. Take it a watch at part examples.

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

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The absolute worth of –5 is 5. The distance from –5 come 0 is 5 units.
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The absolute worth of 2 + (–7) is 5. When representing the sum on a number line, the resulting point is 5 units from zero.
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The absolute worth of 0 is 0. (This is why us don"t say that the absolute value of a number is positive. Zero is neither an adverse nor positive.)

Absolute value Examples and also Equations

The most common method to stand for the absolute value of a number or expression is to surround it v the absolute value 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 unfavorable of the absolute value of x.

The number heat is not just a method to present distance indigenous zero; it"s also a useful way to graph equalities and also inequalities the contain expressions with absolute value.

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Consider the equation |x| = 2. To present x on the number line, you need to show every number who absolute value is 2. There are exactly two locations where the happens: in ~ 2 and also at –2:


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Now think about |x| > 2. To display x ~ above the number line, you require to display every number whose absolute worth is better than 2. As soon as you graph this on a number line, use open dots in ~ –2 and also 2 to show that those numbers space not part of the graph:


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

Now consider |x| ≤ 2. You are trying to find numbers whose absolute worths are 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 also true for all of the the contrary numbers between –2 and 0. Once you graph this top top a number line, the closeup of the door dots at –2 and also 2 show that those numbers room included. This is due to the inequality making use of ≤ (less 보다 or same to) instead of

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Math tasks and Lessons qualities 6-8