Inequalities help?

Question

How do you solve Inequalities with 2 < signs?

Example: 5x<15<60

Answering ASAP would help because I have a big test tomorrow.

Answer 1

In your example the only part that matters is 5x < 15 because if it is < 15 it will automatically be < 60.

So 5x < 15 divide by 3 both sides, and you get x < 3.

If you had a < 5x < b, where a and b are some number then consider each inequality separately. Divide by 5 both sides of each inequality and put them back together, and you would get

a/5 < x < b/5

Answer 2

Both inequalities must be true: in this case,
5x < 15 AND 15 < 60.

Your example isn't particularly good (because 15 < 60 is always true). A better one would be
15 < 5x < 60
which means
15 < 5x AND 5x < 60
<=> 3 < x AND x < 12
<=> x ∈ (3, 12).

You could also have one like
2x - 4 < 10 < x + 18
<=> 2x - 4 < 10 AND 10 < x + 18
<=> 2x < 14 AND -8 < x
<=> x < 7 AND x > -8
<=> x ∈ (-8, 7).

Answer 3

If 5x is lesser than 15 and 15 is also lesser than 60, x could be 2.