Question

How do you solve this absolute value equation and inequality problem?

Answer 1

r > 10 or r < - 7

Explanation:

isolate the absolute value by dividing both sides by - 2

| 3 - 2r | > 17

Inequalities of the type | x | > a always have solutions of the form

x < -a OR x > a, hence

3-2r < - 17 or 3 - 2r > 17 ( subtract 3 from each interval )

- 2r < - 20 or - 2r > 14 ( divide both intervals by - 2 )

Remembering to reverse each inequality symbol as a result of dividing by a negative quantity.

r > 10 or r < - 7

Answer 2

r < -7 or r > 10

Explanation:

-2|3 - 2r| < -34

|3 - 2r| > 17 (Note the inequality sign flips because we divide by negative)

Now we split it up into 2 inequalities :-

3 - 2r > 17

-2r > 14

r < -7 (answer)

and

3 - 2r < -17

-2r < -20

r > 10 (answer).