Interval Notation Practice Problems with Answers

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) [latex]x < 3[/latex]

Answer

[latex]\left( { – \infty ,3} \right)[/latex]

2) [latex]x \ge – 7[/latex]

Answer

[latex]\left[ { – 7,\infty } \right)[/latex]

3) [latex]- 1 < x \le 5[/latex]

Answer

[latex]\left( { – 1,5} \right][/latex]

4) [latex]x < 0[/latex]

Answer

[latex]\left( { – \infty ,0} \right)[/latex]

5) [latex]2 \le x \le 6[/latex]

Answer

[latex]\left[ {2,6} \right][/latex]

6) [latex]x \ge 1[/latex]

Answer

[latex]\left[ {1,\infty } \right)[/latex]

7) [latex] – 10 < x < 0[/latex]

Answer

[latex]\left( { – 10,0} \right)[/latex]

8) [latex]\large{x > {1 \over 2}}[/latex]

Answer

[latex]\left( {{1 \over 2},\infty } \right)[/latex]

9) [latex]\left| x \right| < 4[/latex]

Answer

[latex]\left( { – 4,4} \right)[/latex]

10) [latex]x \ne 0[/latex]

Answer

[latex]\left( { – \infty ,0} \right) \cup \left( {0,\infty } \right)[/latex]


Part 2. Express each phrase as an interval notation.

1) all real numbers greater than [latex]17[/latex]

Answer

[latex]\left( {17,\infty } \right)[/latex]

2) all real numbers less than or equal to [latex]-2[/latex]

Answer

[latex]\left( { – \infty , – 2} \right][/latex]

3) all real numbers between [latex]-3[/latex] and [latex]2[/latex], including [latex]-3[/latex] but not including [latex]2[/latex]

Answer

[latex]\left[ { – 3,2} \right)[/latex]

4) all real numbers greater than [latex]0[/latex]

Answer

[latex]\left( {0,\infty } \right)[/latex]

5) all real numbers greater than or equal to [latex]13[/latex]

Answer

[latex]\left[ {13,\infty } \right)[/latex]

6) all real numbers between [latex]-1[/latex] and [latex]1[/latex], including [latex]-1[/latex] and [latex]1[/latex]

Answer

[latex]\left[ { – 1,1} \right][/latex]

7) all real numbers less than [latex]5[/latex]

Answer

[latex]\left( { – \infty ,5} \right)[/latex]

8) all real numbers between [latex]0[/latex] and [latex]100[/latex], not including [latex]0[/latex] but including [latex]100[/latex]

Answer

[latex]\left( {0,100} \right][/latex]

9) all real numbers that are less than [latex]3[/latex] units from [latex]0[/latex]

Answer

[latex]\left( { – 3,3} \right)[/latex]

10) all real numbers not equal to [latex]-1[/latex]

Answer

[latex]\left( { – \infty , – 1} \right) \cup \left( { – 1,\infty } \right)[/latex]


You might also be interested in:

Interval Notation