How do I solve this inequality?

Question

x-7<3x-5<x+11

Please tell me how to solve it so that I can learn how to do the others. Please don't just put the answer.

Answer 1

Let&#039;s break it up into pieces.  Compare the first two numbers:

x-7&lt;3x-5

You want to get x by itself on one side of the &lt; sign.  Subtract an x from both sides to get -7&lt;2x-5.  Add 5 to both sides to get -2&lt;2x.  Divide by 2 to get x by itself: -1&lt;x

Now compare the middle two numbers:

3x-5&lt;x+11

Again we want to get x by itself.  Subtract x from both sides.  2x-5&lt;11.  Add 5 to both sides.  2x &lt; 16.  Divide by 2 to get x by itself.  x &lt; 8.

So now we know x&gt;-1 and x&lt;8

We can also write this -1&lt;x&lt;8

Answer 2

start by subtracting x from all sides, then add 5 and finally divide by 2

x-7&lt;3x-5&lt;x+11

-7&lt;2x-5&lt;11

-2&lt;2x&lt;16

-1&lt;x&lt;8

Just remember, that whatever you do to one part, you have to do to all parts of the inequality.