Question

Your friend says that the solutions to the inequality 5x - 14x < - 18 are x ≤2. Solve the inequality correctly. What error did your friend
make?

Answer 1

Answer:  x > 2

Work Shown:

5x - 14x < - 18

-9x < - 18

x > -18/(-9)

x > 2

The inequality sign flips when dividing both sides by a negative number.

Here's another approach you could take.

5x - 14x < - 18

-9x < -18

0 < -18+9x

18 < 9x

9x > 18

x > 18/9

x > 2

It's a slightly longer pathway, but it avoids a sign flip when you divide both sides by the positive number 9.

The sign flip happens two steps earlier when going from 18 < 9x to 9x > 18. In other words, A < B is the same as B > A.