Question

Draw a number line and mark on it, if possible, all described points. Numbers that are larger than 2 and smaller than 5.

Answer 1

Explanation:

The number line below describes number larger than 2.

This can be written as {x: x > 2}.

Note that the indicator on 2 is not shaded, this shows that 2 is not included in the set.

..|......|......|......|......|......|......|......|......|......|..

-2....-1.....0....1.....2.....3....4.....5....6.....7

............................O-------------------------->

.......................................(x > 2)

The number line below describes number smaller than 5. This can be written as {x: x < 5}. 5 is not included in this set neither, so, the indicator is also not shaded.

..|......|......|......|......|......|......|......|......|......|..

-2....-1.....0....1.....2.....3....4.....5....6.....7

<-------------------------------------O

...............(x < 5)

LOOK AT THIS EXAMPLE BELOW

..|......|......|......|......|......|......|......|......|......|..

-2....-1.....0....1.....2.....3....4.....5....6.....7

<--------------------------------•

...............(x ≤ 4)

Note that the indicator on 4 is shaded black. It shows that 4 is included in the set.