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.

Step-by-step explanation:

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

$\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5$

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).

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

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

$x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5$

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.