Question

Hey, I need help with solving this inequality. It is for Introductory Algebra (0308) TSI Review. I need to pass the TSI which is 20 to 45 questions long and I have failed it in the past a total of four times, please help me to understand this: -4<4-2x<6

Thanks So Much!

Answer 1

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!