Interval Notation Practice Problems with Answers

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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