Question

Use the form |x – b| < c or |x – b| > c to write an absolute value inequality that has the solution set x= < –9 or x>=-5.

Answer 1

Answer: |x + 9| > 0 or |x + 5| < 4

Step-by-step explanation: To begin with, ready to utilize the frame |x - b| > c to speak to the arrangement x < -9:

|x - (-9)| >

Rearranging this gives:

|x + 9| >

Another, we are able utilize the frame |x - b| < c to speak to the arrangement x ≥ -5. Ready to select a esteem of c that's more noteworthy than the remove from -5 to the closest endpoint of the arrangement set (which is -9):

|x - (-5)| < 4

Rearranging this gives:

|x + 5| < 4

Joining these two supreme esteem disparities with an "or" explanation gives:

|x + 9| > or |x + 5| < 4

Rearranging this gives:

x < -9 or -9 < x < -1

We will see that the primary portion of the arrangement set (x < -9) is as of now spoken to within the to begin with supreme esteem imbalance, and the moment portion (x ≥ -5) is spoken to by the moment supreme esteem imbalance.