When solving absolute value inqualities, if it's less than it's "and", if it's greater than it's "or". what about less than or equal to or greater than or equal to?
A ≤ B is that A is less than or equal to B, which is complement to A > B.
A ≥ B is that A is greater than or equal to B, which is the complement to B > A.
It cannot be both equal to and either less than or more than any value.
I hope this helps. Thanks for asking.
thank you!
When solving absolute value inequalities, the inequality symbols "less than or equal to" (≤) and "greater than or equal to" (≥) also follow the same rules as the corresponding inequality symbols without the "equal to" part.
If the inequality is of the form |x| ≤ a, where 'a' is a positive number, it means that the distance between 'x' and 0 is less than or equal to 'a'. In this case, we consider two separate inequalities:
1. x ≤ a: This represents all the values of 'x' that are less than 'a'.
2. -x ≤ a: We rewrite this inequality as x ≥ -a. This represents all the values of 'x' that are greater than or equal to '-a'.
So, the solution to |x| ≤ a is x ≤ a and x ≥ -a. To find the complete solution set, you can combine both inequalities with the word "and" (for example, x ≤ a and x ≥ -a).
Similarly, if the inequality is of the form |x| ≥ a, it means that the distance between 'x' and 0 is greater than or equal to 'a'. In this case, we have two separate inequalities:
1. x ≥ a: This represents all the values of 'x' that are greater than or equal to 'a'.
2. -x ≥ a: We rewrite this inequality as x ≤ -a. This represents all the values of 'x' that are less than or equal to '-a'.
So, the solution to |x| ≥ a is x ≥ a or x ≤ -a. To find the complete solution set, you can combine both inequalities with the word "or" (for example, x ≥ a or x ≤ -a).