There are twenty (20) problems here that you can use to practice your skill in writing interval notations.
Part 1. Write each inequality as an interval notation.
1) x < 3
Answer
\left( { - \infty ,3} \right)
2) x \ge - 7
Answer
\left[ { - 7,\infty } \right)
3) - 1 < x \le 5
Answer
\left( { - 1,5} \right]
4) x < 0
Answer
\left( { - \infty ,0} \right)
5) 2 \le x \le 6
Answer
\left[ {2,6} \right]
6) x \ge 1
Answer
\left[ {1,\infty } \right)
7) - 10 < x < 0
Answer
\left( { - 10,0} \right)
8) \large{x > {1 \over 2}}
Answer
\left( {{1 \over 2},\infty } \right)
9) \left| x \right| < 4
Answer
\left( { - 4,4} \right)
10) x \ne 0
Answer
\left( { - \infty ,0} \right) \cup \left( {0,\infty } \right)
Part 2. Express each phrase as an interval notation.
1) all real numbers greater than 17
Answer
\left( {17,\infty } \right)
2) all real numbers less than or equal to -2
Answer
\left( { - \infty , - 2} \right]
3) all real numbers between -3 and 2, including -3 but not including 2
Answer
\left[ { - 3,2} \right)
4) all real numbers greater than 0
Answer
\left( {0,\infty } \right)
5) all real numbers greater than or equal to 13
Answer
\left[ {13,\infty } \right)
6) all real numbers between -1 and 1, including -1 and 1
Answer
\left[ { - 1,1} \right]
7) all real numbers less than 5
Answer
\left( { - \infty ,5} \right)
8) all real numbers between 0 and 100, not including 0 but including 100
Answer
\left( {0,100} \right]
9) all real numbers that are less than 3 units from 0
Answer
\left( { - 3,3} \right)
10) all real numbers not equal to -1
Answer
\left( { - \infty , - 1} \right) \cup \left( { - 1,\infty } \right)
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