Question

Please help. Show with steps please.

Solve the compound inequality.

0 < 5-2x/3 <5

Answer 1

Answer: The answer is x < 5/2 and x > -5.

Explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

`(5-2x)/(3) > 0\\(5-2x)/(3) < 5\\`

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

`5-2x > 0*3\\5-2x < 5*3`

`-2x > 0-5\\-2x < 15-5`

`x < (-5)/(-2) =x < (5)/(2) \\x > (10)/(-2) =x > -5`

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.