Question

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

Answer 1

`-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.