Hello!
This one is a little tricky, but easy once you split it into a couple of parts!
So you have your whole inequality:
-4<4-2x<6
Let’s break it into two parts right down the middle. This just makes it way easier to solve! Start with -4<4-2x
Now, solve for “x” in that simple inequality. Remember that the inequality acts just like an equal sign, except for when you divide or multiply by a negative number! Then you have to flip it around.
-4<4-2x
Subtract 4 from each side
-8<-2x
Now, divide by -2 on both sides to get x by itself. Remember you are dividing by a negative in this case, so you have to flip the inequality around once you finish!
4>x
You can rewrite that as x<4 (it means the same thing :)
Now, let’s do the other half of this inequality. We’re doing the same thing, just the other side!
4-2x<6
Solve for x! Subtract 4 from each side
-2x<2
Get x by itself by dividing by -2 on both sides. Remember to flip the inequality since it’s negative!
X>-1
Ok! You’ve solved both parts of this, now it’s time to piece it all together.
You know x is less than 4 based on the first step, but greater than negative one based on the second step! Therefore, you write:
-1
I hope this makes sense! If you have any questions, please let me know!