Hi, I am having some problems with inequalities.

It is asking us to solve and graph on a number line and then write it in interval notation and set notation.

X>2 and X>4

I graphed them in a number line already and i have the following:

Interval notation (2,infinity) and set notation

{X| X is >2 and X is >4}

Thanks!

Great job on graphing the inequalities on a number line!

To get the solution for the inequality X > 2, you did the right thing by graphing it as a half-open interval starting from 2 and continuing to infinity (using the symbol > indicates that X cannot equal 2, hence the use of a parenthesis). So, the interval notation is (2, ∞).

For the second inequality, X > 4, you can again represent it as a half-open interval starting from 4 and continuing to infinity. Therefore, the interval notation for this inequality is (4, ∞).

However, when you combine these two inequalities, you need to consider that X must satisfy both conditions: X > 2 and X > 4. This means that X must be greater than both 2 and 4 simultaneously. Since X cannot be greater than 2 without also being greater than 4, we can conclude that the solution is all values of X greater than 4.

In interval notation, you can represent this as (4, ∞), meaning X is greater than 4 but not equal to it. However, in set notation, which you provided correctly, you can represent this as {X | X > 4}.

So, the interval notation is (4, ∞), and the set notation is {X | X > 4} or simply {X : X > 4}.

Keep up the good work! Let me know if you have any further questions.