Write the set in interval notation.

Question

32.{x | −7 ≤ x ≤ 1}

31.{x | x ≤ 4}

30.{x | −10 < x ≤ 4}

29.{x | x > 1}

Answer 1

For interval notation, ≤ or ≥ uses [ and ] for the symbols.

< and > use ( and ) for symbols. ∞ and -∞ also use ( and ) for symbols.

[-7,1]

(-∞,4]

I will leave the others for you to try, they are similar to these.

Answer 2

(32) Since there is an equal sign under the < sign <, the numbers -7 and 1 are included in the solution, hence we use square bracket for included ends. The answer would be [-7,1]

(33) Since there is an equal sign under the < sign <, number 4 is included in the solution. Since the solution includes all numbers less then 4, them the solution is from "Negative Infinity" to Number 4.

Note: Infinity and Negative Infinity always use regular brackets ( or ) because these ends are not included in the solution. The answer will be ( Negative Infinity , 4 ]

(34) As above, -10 is not included because there is no equal sign under the < , so we use regular bracket. While 4 is included. The answer is (-10,4]

(35) The solution is all the numbers greater than 1, which means 1 up to positive infinity. The answer would be (1, Positive Infinity).