1.5: Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Give examples of numbers that are
- natural numbers
- integers
- integers but not natural numbers
- rational numbers
- real numbers
- rational numbers but not integers
- Answer
-
- 2,3,5
- −3,0,6
- −3,−4,0
- 23,−47,8
- √5,π,3√31
- 12,25,0.75
Which of the following numbers are natural numbers, integers, rational numbers, or real numbers? Which of these numbers are irrational?
- 73
- −5
- 0
- 17,000
- 124
- √7
- √25
- Answer
-
- rational
- integer, rational
- integer, rational
- natural, integer, rational
- natural, integer, rational
- irrational
- natural, integer, rational
All of the given numbers are real numbers
Evaluate the following absolute value expressions:
- |−8|
- |10|
- |−99|
- −|3|
- −|−2|
- |−√6|
- |3+4|
- |2−9|
- |−5.4|
- |−23|
- |5−2|
- −|−−6−3|
- Answer
-
- 8
- 10
- 99
- −3
- −2
- √6
- 7
- 7
- 5.4
- 23
- 52
- −2
Solve for x:
- |x|=8
- |x|=0
- |x|=−3
- |x+3|=10
- |2x+5|=9
- |2−5x|=22
- |4x|=−8
- |−7x−3|=0
- |4−4x|=44
- −2⋅|2−3x|=−12
- 5+|2x+7|=14
- −|−8−2x|=−12
- Answer
-
- S={−8,8}
- S={0}
- S={}
- S={−13,7}
- S={−7,2}
- S={−4,245}
- S={}
- S={−37}
- S={−10,12}
- S={−43,83}
- S={−8,1}
- S={−10,2}
Solve for x using the geometric interpretation of the absolute value:
- |x|=8
- |x|=0
- |x|=−3
- |x−4|=2
- |x+5|=9
- |2−x|=5
- Answer
-
- S={−8,8}
- S={0}
- S={}
- S={2,6}
- S={−14,4}
- S={−3,7}
Complete the table.
Inequality notation | Number line | Interval notation |
---|---|---|
2≤x<5 | ||
x≤3 | ||
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||
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||
[−2,6] | ||
(−∞,0) | ||
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||
5<x≤√30 | ||
(137,π) |
- Answer
-
Inequality notation Number line Interval notation 2≤x<5 [2,5) x≤3 (−∞,3] 12<x≤17 (12,17] x<−2 (−∞,−2) −2≤x≤6 [−2,6] x<0 (−∞,0) 4.5≤x [4.5,∞) 5<x≤√30 (5,√30] 137<x<π (137,π)
Solve for x and write the solution in interval notation.
- |x−4|≤7
- |x−4|≥7
- |x−4|>7
- |2x+7|≤13
- |−2−4x|>8
- |4x+2|<17
- |15−3x|≥6
- |5x−43|>23
- |√2x−√2|≤√8
- |2x+3|<−5
- |5+5x|≥−2
- |5+5x|>0
- Answer
-
- S=[−3,11]
- S=(−∞,−3]∪[11,∞)
- S=(−∞,−3)∪(11,∞)
- S=[−10,3],
- S=(−∞,−52)∪(32,∞)
- S=(−194,154)
- S=(−∞,3]∪[7,∞)
- S=(−∞,215)∪(25,∞)
- S=[−1,3]
- S={}
- S=(−∞,∞)=R
- S=(−∞,−1)∪(−1,∞)=R−{−1}