Question

What are the solutions of /x+6/is greater than or equal to 5. Write the solutions as either the union or the intersection of two sets.

Answer 1

the intersection of two sets?????

Answer 2

x+6 can be negative or positive. Which case this is, will change how the absolute value works. This leads to two different sets of solutions:

x+6 <= -5, and 5 >= x+6.

If you look the number line for these two possibilities, then you'll see that if x satisfies either of these two equations, then it satisfies |x+6| >= 5.

This tells you that you want the union of the sets of solutions to the two equations.

Answer 3

-11 U -1 ????

Answer 4

Almost. But you want *all* values of x that satisfy the two equations. For the second equation, -1+6=5, which is greater than or equation to five. But if x is any number larger than -1, then the equation will also be satisfied. So for the second equation, any x in [-1, infinity) will do.

Answer 5

I mean the second inequality*

Answer 6

When you solve an inequality like this, you can kind of treat it like an equality, to find the boundary points to the set, and then figure out which direction you can let the set run off to.