Please show me how to put this in interval notation. Thanks!
I know I solved this right, I think, but need to put it in interval notatioin. Please tell me if i am correct. Thanks!
PleaseSolve: (x-3)/(x^2-25)<0 and write solution set in interval notation. This is what I get:
x<-5 or 3< x <5
And in interval notation?
In interval notation, we combine two disjoint intervals with the union operator, ∩. Therefore the answer in interval notation would be:
(-∞, -5) ∩ (3,5)
Parentheses are used (instead of square brackets) to indicate that the limits are excluded from the intervals. Some interval notations use square brackets facing towards the exterior (=exclude) instead of parentheses, i.e.
]-infin;, -5[ ∩ ]3,5[
]-∞, -5[ ∩ ]3,5[
Sorry, the union operator is ∪
so the correct intervals are:
(-∞,-5) ∪ (3,5)
or
]-∞, -5[ ∪ ]3,5[
To express the solution set in interval notation, you follow a standard format using brackets and parentheses.
Given the solution set x < -5 or 3 < x < 5, you can represent it in interval notation as follows:
1. For the interval x < -5: The solution set includes all real numbers that are less than -5. To represent this, you would use the notation (-∞, -5).
2. For the interval 3 < x < 5: The solution set includes all real numbers that are greater than 3 and less than 5. To represent this, you would use the notation (3, 5).
Therefore, the entire solution set, expressed in interval notation, would be (-∞, -5) ∪ (3, 5).
In other words, the solution set consists of all real numbers less than -5, excluding -5 itself, and all real numbers between 3 and 5, excluding both 3 and 5.