Solve and graph the solution to the compound inequality.

Question

−4x ≥ 36 or x − 7 ≥ −3


(1 point)

Answer 1

To solve the compound inequality, we will solve each inequality separately and then combine the solutions.

First, let's solve the inequality -4x ≥ 36:
Dividing both sides by -4 (remembering to reverse the inequality when dividing by a negative number), we have:
x ≤ -9

Now let's solve the inequality x - 7 ≥ -3:
Adding 7 to both sides, we have:
x ≥ 4

Now, let's combine the solutions:
The solution to the compound inequality is x ≤ -9 or x ≥ 4.

To graph the solution on a number line, we draw a number line and mark -9 and 4 with open circles (since the inequalities are "greater than or equal to" and "less than or equal to"). Then, we shade the area to the left of -9 and the area to the right of 4, including the two points.

Here is the graph:
<=========o====[<------------------]====o===>
-9 4