Preliminary Mathematics Worksheet
Equations with Absolute Values
NSW Syllabus Ref: 1.4

© Mathematics Plus, 2002


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1.    Evaluate:

I

II

III

(a)

|-5|

(a)

|4 - 8|

(a)

|-2 - 3|

(b)

|-2| + |-3|

(b)

|3| - |-3|

(b)

|-5| - |-6 + 1|

(c)

|-4| ´ |-5|

(c)

|-16| ¸ |-3 - 1|

(c)

0.5 ´ |-4|

(d)

|-4|2

(d)

|-2|2 - |-1|2

(d)

|-2|3 - |-3|3

(e)

|Ö2 - 2|

(e)

|3 - p|

(e)

|0| - |1 - Ö2|




2.   True or false?

I

II

(a)

|-3| ´ |-4| = |3 ´ 4|

(a)

|-10| + |-5| = |-10 - 5|

(b)

|-7| + |7| = |-7 + 7|

(b)

|-4| + |5| = |(-4) + (-5)|

(c)

|x| = |-x|

(c)

|x| = -|-x|

(d)

|a2| = a2

(d)

|x2| = |x|2

(e)

|x2 + 1| = x2 + 1

(e)

|a2 - 2| = a2 + 2

(f)

|x + y| = |x| + |y|

(f)

|x - y| = |y - x|

(g)

|2a| + |2b| ³ 2|a + b|

(g)

|3a| + |-3b| ³ 3|a + b|

(h)

If |x| < 1 then 0 < x2 < 1

(h)

|a ´ b| ³ a ´ b




3.    Solve these equations:

I

II

III

(a)

|x| = 2

(a)

|x| - 6 = 0

(a)

|x| = 0

(b)

|x + 1| = 2

(b)

|x - 2| = 2

(b)

|1 - x| = 1

(c)

|2x| = 6

(c)

|2x + 1| = 3

(c)

|x| = -1

(d)

|3x - 4| = 5

(d)

|4 - 3x| = 5

(d)

3 - |2x + 3| = 0

(e)

|5x - 10| = 0

(e)

|6 + 2x| = 2

(e)

|1 - 3x| = 1/2

(f)

|2x - 3| = |x + 6

(f)

|x + 1| = |x - 1|

(f)

|x + 2| = 2|x + 2|

(g)

|3x + 2| = |4x - 9|

(g)

|5x + 2| = |2x - 1|

(g)

|7x - 2| - 3|x - 4| = 0

(h)

|5 + x| = |-x|

(h)

3|x + 3| = 2|x + 2|

(h)

2|x + 1| - 6|x + 3| = 0




4.    Solve these equations (remember to check the validity of each solution):

I

II

III

(a)

|x + 1| = 2x + 3

(a)

|x - 2| = x

(a)

|2 - 3x| = 5 - 6x

(b)

|10x - 3| = 2x + 5

(b)

|1 - 6x| = 2x + 9

(b)

3x + 5 = |5x - 3|

(c)

|x + p| = 2x - p

(c)

|3x - 2| - 5x + 4 = 0

(c)

|4 - 3x| + 3x = 2




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