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So far, we've just been solving inequalities with two parts: a left side and a right side like this

5x > 2x - 7

But, sometimes we'll have inequalities with three parts:

-3 is less than or equal to 2x - 1 is less than or equal to 5

Sometimes, these are called compound inequalities.

So, what do we do on these?

Our goal is the same:

Get the x alone!

On these, we just get him alone in the middle section.  So, just like before, pretend that there are really = signs and go about your business...  We'll just be working all three sections at once.

Let's go:

-3 is less than or equal to 2x - 1 is less than or equal to 5

Get the x alone in the middle...

                           -3 is less than or equal to 2x - 1 is less than or equal to 5, ditch the -1 by adding 1 to all three parts which gives -2 is less than or equal to 2x is less than or equal to 6, ditch the 2 by dividing each part by 2 which gives -1 is less than or equal to x is less than or equal to 3
 

number line showing x is greater than or equal to -1 and x is less than or equal to 3

[ -1 , 3 ]

But, what does this mean?

x can be -1... or x can be 3...or x can be a number between -1 and 3... like 0 or 2.315.