Question

Help..........

Answer 1

\[2x-1\le 3x-5\le x+9\]

Answer 2

ok...do you understand what i meant by taking them in pairs?

Answer 3

umm...not really..

Answer 4

ok...then we start there :)

The trick here is to split the problem up since we can't work it the way it is...

We are going to make 2 inequalities and work on them individually...

Start by taking the left hand binomial and the middle binomial...that is
\[2x-1\le 3x-5\]
that's the first one...then take the middle and the right ones...that is
\[3x-5 \le x+9\]

Those are the two inequalities we need to solve...then we'll worry about putting it all back together later.

with me so far?

Answer 5

Yes. I am. Makes sense and clear!!:)

Answer 6

good :) now, how are you with solving these two? do you need me to go through one and you try the other? or do you think you can do them and i'll check your work?

Answer 7

Umm...I'll try one one on my own. If i don't get the right answer..then just walk me through the step..

Answer 8

absolutely... :)

Answer 9

Umm....I'm kind of stuck..lol...Whatever..just walk me through one...then...i'll do one on my own..

Answer 10

I got..\[3x \le x+14\]

Answer 11

you're almost there...move the x to the left...by subtracting x from both sides

Answer 12

remember...x is a number just like 5, the only difference is that we don't know what it is...but anything you can do with numbers, you can do with x...

Answer 13

Ok. After moving that..I got..\[2x \le 14\]
I know that simplifys to 7....when dividing by 2 from both sides.

Answer 14

right, so you have \[x \le 7\] for the second inequality on our list... :)

Answer 15

so far so good?

Answer 16

Yes. Do you want me to solve the nest one?? And then you check??

Answer 17

sounds like a great idea

Answer 18

Ok. I got..\[4\le x\]

Answer 19

perfect! :)

Answer 20

now we need to put it all back together...

Answer 21

How would I put them together now?

Answer 22

since you have the inequalities facing the same direction...meaning you have
\[4 \le x\] and \[x \le 7\] just put the x's on top of each other...
\[4 \le x \le 7\]

Answer 23

Wait..Why wouldn't it be \[x^2\] ??

Answer 24

Basically, what we established is that x must be a number less than or equal to 7 (from the first one we worked) *and* greater than or equal to 4 (from the second one...

So x must be between 4 and 7...inclusive of 4 and 7...

Answer 25

because we aren't multiplying...just putting the pieces back after the split

Answer 26

Oh..Ok...Makes clearly sense...Thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:) I love how you guided me to the end of the solution and explained it to me!!:) Thanx again!!!:)

Answer 27

my pleasure...thank you for following the path and wanting to learn instead of just looking for the answer :)

Answer 28

I also have one similar to this one...But i'll close this and post a new one....(if you don't mind i'll work it out and tell me if i got it right...) is that fine with you??

Answer 29

perfectly fine...i'm here for another 30 minutes or so...

Answer 30

Alright!!:) Quick....lol...