Question

16 < 2x + 4 < 4

Answer 1

These are really confusing. I've never done one like this before, @Mertsj @jim_thompson5910 Can you help?

Answer 2

You want to isolate x, so your first step is to move that +4 away from the 2x

You do this by subtracting 4 from each side


16 < 2x + 4 < 4
-4 -4 -4



12 < 2x < 0

Answer 3

first you solve 16 < 2x + 4, then solve 2x + 4 < 4.
How?
Treat the < as an =

16 < 2x + 4
12 < 2x
6 > x (You MUST switch the sign if you are dividing)

And again:
2x + 4 < 4
2x < 0
x > 0

So the answer is: 6 > x > 0
To graph it, draw a number line, let's say from 0 to 10. The value of x is bigger than 0 but less than 6. This means x cannot be 0 or 6. Since your signs are greater than, not greater than or equal to, form an open (unshaded) circle over the 0 on your number line, and do the same for 6. Now draw a dark line between the two circles to show that the value of x lies in between.
reference:

Answer 4

So after you get 12 < 2x < 0, your next step is to divide each side by 2 to fully isolate x


\[\Large 12 < 2x < 0\]

\[\Large \frac{12}{2} < \frac{2x}{2} < \frac{0}{2}\]

\[\Large 6 < 1x < 0\]

\[\Large 6 < x < 0\]

Answer 5

Because we got the answer \[\Large 6 < x < 0\], I'm assuming that there are negative signs missing in the original problem

Answer 6

No negative signs are in the original problem.

Answer 7

since it's not possible to have a number that's larger than 6 AND less than 0 at the same time

Answer 8

So there are no solutions then. This is assuming that there are no typos

Answer 9

So I would just wright "No solutions"?

Answer 10

that's what I would do

Answer 11

of course you have to show why there are no solutions

Answer 12

write* WOW, Horrible grammar mistake there, sorry.

Answer 13

its fine lol

Answer 14

don't have to be write all the time

Answer 15

So, I would just show my work to explain why there is no solution?

Answer 16

yes exactly

Answer 17

Awesome, Okay. Thanks!

Answer 18

you're welcome