Set Operation: Union - Problem 1

The union of two linear inequalities. So for this one what we actually have to do is first solve our both of these inequalities by themselves just as we would any other linear inequality. Lucky these are pretty straight forward so just to solve for x subtract 2, x is less than or equal to 5 so this one subtract 2, x is greater than or equal to -6 and we are dealing with the union of these two things.

For anytime we are dealing with inequalities I almost always make a number line, it helps me see what’s going on. So make a number line we have the number 5 and we also have the number -6. In general I will write it off the number line so I can just sort of instead of laying things on top of each other I can see individually what’s happening. So this is saying x is less than or equal to 5 so we have a closed in circle and we are shading down.

For this one x is greater than or equal to -6 we have a closed in circle at -6 and for this time we are going up. Remember union is as long as it’s in one set, it's a union. So looking at this number line over here numbers less than -6 there is something in this set that’s covered by the x is less than 5. So this part is in our union.

Looking at the middle between -6 and 5, both of our inequalities are here so that’s in the union as well remember as long as 1 is there it's good and lastly this part greater than 5 there’s is an element as well dealing with numbers that would be relating with this one, so again there’s at least one thing represented there.

So everywhere in this line there’s something in this union so you can write that all your numbers are in this union or negative infinity to infinity if you want to do interval notation either one works.