Example: "boxes approximately 20 kg in mass are allowed"

If your box is exactly 20 kg ... will certainly that be allowed or not?

It isn"t really clear.

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Let"s check out exactly how to be precise around this in each of three popular methods:

Inequalities The Number Line Interval Notation


With Inequalities we use:

> greater than≥ better than or equal to much less than≤ less than or equal to

Like this:

Interval Notation

In "Interval Notation" we just compose the beginning and finishing numbers of the interval, and use:

< > a square bracket once we want to include the end worth, or( ) a round bracket as soon as we don"t

Like this:


Number Line

With the Number Line we draw a thick line to present the worths we are consisting of, and:

a filled-in circle as soon as we want to encompass the finish worth, oran open circle as soon as we don"t

Like this:



suggests all the numbers in between 0 and also 20, carry out not encompass 0, however do encompass 20

From 1To 2
Including 1Not Including 1Not Including 2 Including 2
Inequality:x ≥ 1 "higher than or equal to"x > 1 "higher than" x "less than" x ≤ 2 "much less than or equal to"
Number line:
1" width="70" height="55" />
, and not incorporate 2:


x ≥ 1 and x

or together: 1 ≤ x

Number line:

That means as much as and including $10.

And it is fair to say all prices are more than $0.00.

As an inequality we display this as:

Price ≤ 10 and also Price > 0

In fact we could combine that into:

0 (0, 10>

Example: x better than, or equal to, 3:

<3, +∞)


Example: x ≤ 2 or x >3

On the number line it looks choose this:


And interval notation looks prefer this:

(-∞, 2> U (3, +∞)

We offered a "U" to suppose Union (the joining together of two sets).

Note: be careful via ineattributes choose that one. Don"t try to join it into one inequality:

2 ≥ x > 3


that doesn"t make feeling (you can not be much less than 2 and also greater than 3 at the very same time).

Union and also Intersection

We just witnessed how to join two sets utilizing "Union" (and the symbol ∪).

There is likewise "Intersection" which suggests "has to be in both". Think "wright here perform they overlap?".

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The Intersection symbol is an upside down "U" prefer this:

Example: (-∞, 6> ∩ (1, ∞)

The initially interval goes up to (and including) 6

The second interval goes from (however not including) 1 onwards.


The Intersection (or overlap) of those two sets goes from 1 to 6 (not consisting of 1, consisting of 6):

(1, 6>

Footnote: Geometry, Algebra and Sets

You may not have actually noticed this ... yet we have actually actually been using: