Question

Which graph shows the solution of 9 – c < 2 or –3c > 15?

Answer 1

To find the solution of the inequality 9 – c < 2 or –3c > 15, we can solve each inequality separately and then combine the solutions.

For the first inequality, 9 – c < 2, we subtract 9 from both sides:
-c < 2 – 9
-c < -7

To make the coefficient of c positive, we multiply both sides by -1 (while flipping the inequality sign):
c > 7

So the solution for the first inequality is c > 7.

For the second inequality, –3c > 15, we divide both sides by -3 (and flip the inequality sign):
c < -15 / -3
c < -5

So the solution for the second inequality is c < -5.

To find the combined solution, we can look for the overlapping regions on a number line graph.

Marking the solutions for each inequality, we have:
c > 7 (everything to the right of 7)
c < -5 (everything to the left of -5)

When we combine these regions, the overlapping part is the empty region. There is no number that is simultaneously greater than 7 and less than -5.

Thus, the graph that represents the solution is an empty graph, indicating that there is no solution.