Question

Solve the compound inequality. Graph the solutions. -5 < 2p - 3 <= 9

Answer 1

We can solve this compound inequality by working on each inequality separately and then taking the intersection of their solutions.

Starting with the left inequality -5 < 2p - 3:
Adding 3 to both sides gives us: -2 < 2p
Dividing both sides by 2 gives us: -1 < p

Now, let's solve the right inequality 2p - 3 <= 9:
Adding 3 to both sides gives us: 2p <= 12
Dividing both sides by 2 gives us: p <= 6

So, now we have the solution:
-1 < p <= 6

To graph this solution, we'll draw a number line with an open circle at -1 to represent the "<" inequality, and a closed circle at 6 to represent the "≤" inequality. Then we'll shade the portion of the number line between -1 and 6.

Here's a rough sketch of the graph:
-1 0 1 2 3 4 5 6
----o----|----|----|----|----|----o----

The shaded region should be between the two points "-1" and "6" on the number line.