Solve each inequality, then graph on the number line.
3p≤-21
To solve the inequality 3p ≤ -21, we will first isolate the variable p.
Step 1: Divide both sides of the inequality by 3:
(3p)/3 ≤ (-21)/3
Simplifying:
p ≤ -7
Now we can graph the solution on a number line.
First, draw a horizontal line and mark a point at -7.
----|---|---|---|---|---|---|---|---|---|---
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Since the inequality is less than or equal to (-7), we need to include the endpoint. You can use an open or closed dot to indicate this:
----|---|---|---|---●---|---|---|---|---|---
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Finally, shade the region to the left of -7 to represent all solutions to the inequality:
----|---|---|---●---|---|---|---|---|---|---
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
This graph represents all values of p that make the inequality 3p ≤ -21 true.