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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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Produced by Dr T