The absolute value of 4-x>14. Is this a disjunction or a conjuction?I know I already asked this question but I don't kow how to tell if this is an and problem or if it is an or problem.
To determine whether the inequality |4 - x| > 14 is a disjunction (or problem) or a conjunction (and problem), we need to analyze the mathematical statement it represents.
First, let's understand the absolute value function. The absolute value of a number is the distance that number is from zero on the number line. Therefore, |4 - x| represents the distance between the number x and 4.
Now, let's analyze the inequality itself: |4 - x| > 14. This inequality states that the distance between x and 4 is greater than 14. In other words, it implies that the value of x is either more than 14 units away from 4 to the right side of the number line or more than 14 units away from 4 to the left side of the number line.
For example, if x = 20, then the distance between x and 4 is 16, which is greater than 14. Similarly, if x = -10, then the distance between x and 4 is 14, which is also greater than 14. Therefore, this inequality is a disjunction (or problem) because it allows for multiple solutions: any value of x that is either less than -10 or greater than 20 would satisfy the inequality.
In summary, the inequality |4 - x| > 14 is a disjunction because it allows for multiple solutions and represents an "or" problem.