We can see a closed circle at -2. This means that x has to be greater than or equal to -2.
- 2≤ xWe can also see an open circle at 3, which means x has to be less than 3.
x< 3
In order to determine which signs we should use to fill the two gaps, we will try to isolate x from each part of the given compound inequality. Let's start with the first one.
We found before that x<3. Notice that we never divided or multiplied by a negative number. This means that the inequality sign stayed the same direction throughout solving it.
x 3 ⇒ x < 3
Let's solve the second inequality.
We found before that -2≤ x. Again, we did not divide or multiply by a negative number, so the inequality sign stayed the same direction throughout.
- 2 x ⇒ -2 $≤$ x
