5 < 5x-2 < 9    find x values

Expert Answers
pohnpei397 eNotes educator| Certified Educator

You can find the answer to this just as if it were a regular equation and not an inequality.  You just isolate the x term and solve for it.  Here are the steps:

First, you must add two to all sides so as to get that term out of the middle.

7 < 5x < 11

Now, divide all sides by 5 to get x in the middle.

7/5 < x < 11/5

Now, let's test this by plugging values into the original equation.  Let's take x = 2, which should be a possible value.

5< 10 - 2 < 9

That's true.

Now let's take x = 3, which should not be a possible value.

5 < 13 < 9

Not true.

So we got the right answer.

hala718 eNotes educator| Certified Educator

5<5x-2<9

To find x values we need to solve the inequality the same way we solve the equation with one variable.

We need to keep x by itself. First we add 2

--> 5+2 < 5x-2+2 < 9+2

--> 7<5x< 11      Now divide by 5

--> 7/5<x<11/5

then x velues belong to the interval (7/5, 11/5) 

7/5<x< 11/5