all number less than 3 units from 0
I need to write inequality represents each situation
| x | < 3
or
-3 < x < 3
To represent the set of all numbers that are less than 3 units from 0, we can use the inequality:
|x| < 3
Here's how you can understand and derive this inequality:
1. Start by considering the absolute value of a number, denoted by |x|. The absolute value is the distance of a number from zero on a number line.
2. The phrase "less than 3 units from 0" means that the distance from any number to zero should be less than 3.
3. Putting it all together, the inequality |x| < 3 represents all numbers x that are less than 3 units away from 0. In other words, it includes all numbers between -3 and +3 on the number line but excludes the values of -3 and +3 themselves.
Therefore, the inequality |x| < 3 represents the situation where all numbers are less than 3 units from 0.