Question

1) |x| < 2; 2) |x| > 3; 3) |x| > 5; 4) |x| < 4; 5) |x| > 6; 6) |x| < 2

Answer 1

1) |x| < 2 = |1|
2) |x| > 3 = |4| 
3) |x| > 5 = |6| 
4) |x| < 4 = |3| 
5) |x| > 6 = |5| 
6) |x| < 2 = |1|  

Answer 2

1. The solution set for the inequality |x| < 2 is all real numbers between -2 and 2, excluding -2 and 2. In interval notation, this can be written as (-2, 2).

2. The solution set for the inequality |x| > 3 is all real numbers less than -3 or greater than 3. In interval notation, this can be written as (-∞, -3) U (3, ∞).

3. The solution set for the inequality |x| > 5 is all real numbers less than -5 or greater than 5. In interval notation, this can be written as (-∞, -5) U (5, ∞).

4. The solution set for the inequality |x| < 4 is all real numbers between -4 and 4, excluding -4 and 4. In interval notation, this can be written as (-4, 4).

5. The solution set for the inequality |x| > 6 is all real numbers less than -6 or greater than 6. In interval notation, this can be written as (-∞, -6) U (6, ∞).

6. The inequality |x| < 2 is equivalent to the inequality -2 < x < 2. Therefore, the solution set for this inequality is the same as the solution set for -2 < x < 2, which is (-2, 2).