Question

Solve the following absolute value inequality |7x| < 21

Answer 1

-3 < x < 3

Explanation:

• Absolute value will convert any negative to a positive. For instance, |-2| = 2

`\left|7x\right| < 21\\`

• Reorder all possible values

`-21 < 7x < 21`

• Consider

`7x > 21\:and\:7x < -21`

`(7x)/(-21)\:and\:(7x)/(21)\\= -3\:and\:3\\x > -3\:and\:x < 3`

• Using this info, that would mean that x could be any value between -2 and 2. Reorder to find the solution.

`-3 < x < 3`

Hope this helps!