Middle Years

# 1.09 Absolute value

Worksheet
Absolute values
1

Consider the number line below:

a

How far is the number 3 from 0?

b

Hence, state the value of |3|.

c

How far is the number - 7 from 0?

d

Hence, state the value of |-7|.

2

Describe what the absolute value of - 5 represents on a number line.

3

State whether the following have a value of \left| - 37 \right|:

A

Both 37 and - 37

B

- 37 only.

C

37 only.

4

Determine whether the following have a value of 37:

A

Both 37 and - 37

B

- 37 only.

C

37 only.

5

Evaluate the following:

a
\left|6\right|
b
\left|65\right|
c
\left|3341\right|
d
\left| - 3 \right|
e
\left| - 67 \right|
f
\left| - 155 \right|
g
\left|11\right|
h
\left|-21\right|
i
\left|-1000\right|
j
\left| - 19 \right|
k
\left| - 756 \right|
l
\left| 8 \right|
6

Evaluate the following:

a
|-2|+|5|
b
|-2+5|
c
|8 - (-6)|
d
|8|-|-6|
e
|-3| + |-7|
f
|-3+(-7)|
g
|8-9|+|-6+4|
h
|9-11|-|-8+5|
7

Evaluate the following:

a
|-3|\times |4|
b
|-3 \times 4|
c
|10 \times (-2)|
d
|12| \div |-4|
e
|-8| \times |-4|
f
|-8 \times (-4)|
g
|6-8|\times |-7+4|
h
\left|\dfrac{5-7}{-4+(6)} \right|
i
\left|\dfrac{18-10}{3-7} \right|
j
\dfrac{|6-12|}{3-4}
8

If |a|=6, what values could a be equal to? Explain your answer.

9

Find the possible values of x for each of the following:

a
|x|=9
b
|x|=4
c
|x|=2
d
|x|=7
e
|x|=11
f
|x|-8=0
g
|x| - 10=0
h
|x|-3=1