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# what is X if -1<9+X<17

what is X if -1<9+X<17

If you have a equation, you are able to add or subtract the same number from each side.  In a three part inequality, you are allowed to add or subtract the same thing from each section.  In this case, we can subtract 9 from all three parts.

-1 < 9 + X < 17

-1 -9 < 9 + X -9 < 17 -9

-10 < X < 8

X can be anything between -10 and 8, not including -10 and 8
.

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: