Solve the compound inequality and choose the correct answer below.

Question

-2x+9<13 or -3x-1>8
what does the numberline look like?

Answer 1

To solve the compound inequality -2x + 9 < 13 or -3x - 1 > 8, we need to solve each inequality separately and then combine the solutions.

For the first inequality: -2x + 9 < 13
Subtract 9 from both sides:
-2x < 4
Divide by -2 (remember to flip the inequality sign when dividing by a negative number):
x > -2

For the second inequality: -3x - 1 > 8
Add 1 to both sides:
-3x > 9
Divide by -3:
x < -3

So, the solutions to the compound inequality are: x > -2 or x < -3

On a number line, this would look like:

---------------------o---o-----------------------------------

where the open circles indicate that -2 and -3 are not included in the solution set.