Question

Solve the absolute value inequality: |4 - e| < 5

Then describe the graph of the solution. (Are the starting points open or closed? Where are the starting points located on the number line? Which way will the lines point?)

Answer 1

(assuming e is a variable)
|4 - e| < 5
There are 2 possible cases:
4 - e < 5
-4 + e < 5
Solve both.

4 - e < 5
We're multiplying the variable by a negative, so flip the inequality sign.
4 - e > 5
4 - e - 4 > 5 - 4
-e > 1
-e / -1 > 1 / -1
e > -1

-4 + e < 5
-4 + e + 4 < 5 + 4
e < 9

e > -1 and e < 9
-1 < e and e < 9
-1 < e < 9

Your answer is {e | -1<e<9}.