Answer :
Answer:
The compound inequality to represent all numbers between -4 and 6 is,
represented by the set A = {x| -4 ≤ x ≤ 6}
Step-by-step explanation:
The compound inequality to represent all numbers between -4 and 6 is,
represented by the set A = {x| -4 ≤ x ≤ 6}.
The above inequality is compound since it involves 2 '≤' symbol.
Answer:
A compound inequality is when it has two inequality sings. This is used to represent intervals, a set of number between two limits. In this case, we need to represent a set of numbers between -4 and 6. It's important to consider that "between" means that -4 and 6 are not included, so we want to represent all numbers more than -4 and less than 6.
So, the first part "all numbers more than -4" can be represented in two ways: x > -4 or -4 < x, both ways represents the same thing, but in this case we are gonna use -4 < x, because it's a compound inequality, where the "x" is always in the middle.
On the other hand, we have "less than 6", this can be also represented in two ways: x < 6 or 6 > x. Now, we need to use the first expression, because to form the compound inequality we need the right side limit.
Therefore, the final compound inequality would be:
-4 < x < 6
Just remember, a compound inequality has a right side limit, and a left side limit. So, in this case the expression is saying considering all numbers between -4 and 6.
Now, we just need to apply an operator that indicates that the compound inequality is for all numbers between those limits. That universal operator is [tex]\forall[/tex].
At last, the final expression would be:
[tex]\forall x:-4 < x < 6[/tex].