Examples with solutions for The Number Line with Signed Numbers: Place on the axis

Exercise #1

A negative number is greater than (-6).

Express the number in terms of b.

-7-7-7-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2111000-1-1-1

Video Solution

Step-by-Step Solution

First, we'll mark on the axis the expression b < 0

-3-3-3-2-2-2-1-1-1000111-4-4-4-5-5-5-6-6-6-7-7-7

Then we'll mark on the axis the expression b > -6

-3-3-3-2-2-2-1-1-1000111-4-4-4-5-5-5-6-6-6-7-7-7

We'll mark in orange the segment representing the requested expression:

-3-3-3-2-2-2-1-1-1000111-4-4-4-5-5-5-6-6-6-7-7-7

0 > b > -6

Answer

0 > b > -6

Exercise #2

Express a number that is greater than 3 but less than 7 in terms of a.

000111222333444555888777666

Video Solution

Step-by-Step Solution

First, we'll mark on the axis the expression a > 3

000111222333444555888777666

Then we'll mark on the axis the expression a < 7

000111222333444555888777666

We'll mark in orange the segment representing the requested expression:

000111222333444555888777666

3 < a < 7

Answer

3 < a < 7

Exercise #3

The expression c is a negative number greater than (-9) and less than (-1) . Write it in mathematical language and mark it on the number axis.

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Video Solution

Step-by-Step Solution

First, we'll mark on the number line the expression C < 0

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Then we'll mark C > -9

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

And finally C < -1

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Now we can see that the section marked in orange overlaps with the expressions we marked:

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

The numbers that create the overlapping section start from -9 to -1 and represent the requested expression:

-9 < c < -1

Answer

-9 < c < -1

Exercise #4

a is a positive number less than 5.

Where is a on the number line?

-3-3-3-2-2-2-1-1-1000111222555444333

Video Solution

Step-by-Step Solution

First, let's mark on the axis the expression a < 5

-3-3-3-2-2-2-1-1-1000111222555444333

Now let's mark on the axis the expression

a > 0

-3-3-3-2-2-2-1-1-1000111222555444333

Let's mark in orange the overlapping segment that represents the requested expression:

-3-3-3-2-2-2-1-1-1000111222555444333

0 < a < 5

Answer

0 < a < 5