How do you graph and solve # absx<=3#?

1 Answer

Answer:

#-3<=x<=3#. See below on how to graph it.

Explanation:

When working with absolute values, remember that no matter the sign inside the absolute value function, it will always return a positive number.

If we had #absx=3#, we would have as solutions #x=3# and #x=-3# (because the negative sign is eliminated by the absolute value function).

We're asked for the range of values where #absxle3#. 0 is a solution, as is 1, as is #-1#. In fact, all the values between 3 and #-3# are solutions:

#-3<=x<=3#

So there's our solution. To graph, we take the number line and put filled in dots on 3 and #-3# (to indicate they are part of the solution) and then draw a line segment connecting the two.