Solving inequalities is very much like solving equations!

If you had **9 + x = 17 **, you would subtract 9 from both sides, and get** x = 8** , no problem.

If you have **9 + x < 17 **, you do the same thing! Subtract 9 from both sides, and get
**x < 8** !

The problem you have is **-1 < 9 + x < 17** . This looks harder, but it's not! You can subtract nine from all THREE sides, and get
**-10 < x < 8** .

Answer: -10 < x < 8

Alternatively, you can rewrite the original problem as two seperate problems: **
-1 < 9 + x** AND **9 + x < 17** .

Rewrite: -1 < 9 + x and 9 + x < 17

Solve them seperately just as you would a normal equation, subtracting 9 from both sides. You get
**-10 < x** AND **x < 8** . You can then put them back together, and get
**-10 < x < 8 **.

Answer: -10 < x < 8

Both methods work fine, and get the same answer. The first one has less steps, and is a little bit faster, but the second one can be easier to look at. I definitely recommend it if you're having trouble with larger, messier problems!

**You're done!** I've included another example that I hope will help with inequalities in general, if you're having trouble with other problems:

In general, solving inequalities is exactly the same as solving equations. The only difference is when you multiply or divide with a negative number! When you do this, you must switch the direction of the inequality sign.

Example:

-2x < 6

If this were an equation, you would have -2x = 6 . You divide both sides by -2, and get x = -3 . No problem!

With the inequality, -2x < 6 , you MUST SWITCH THE SIGN. Divide both sides by -2, as before, but also
**switch the less-than to a greater-than**:

answer: x **>** -3

That's really all there is to inequalities!