Inequality Solution

by Nic
(Michigan)

I need help solving the following inequality:
-4<3-2x<20

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Jan 13, 2010
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by: Karin

Hi Nic,

This type of inequality requires a few more steps in order to solve. The following is a step by step solution:

Your goal is to get x by itself in the middle of the inequality. Therefore, you need to get rid of the constant, 3 and the coefficient -2.

We will use the rules that you are familiar with for solving equations and inequalities:

1. Whatever you do to one side, you must do to the other side. In this case, whatever you do to the "middle" you must do to both sides of the inequality.

2. If you multiply or divide by a negative number, you must reverse the inequality sign.

Step 1: Subtract 3 from the middle and "both sides".

-4 -3 < 3 - 3 - 2x < 20-3

Step 2: Simplify

-7 <-2x < 17

Step 3: Divide the middle and "both sides" by -2.

-7/-2 < -2x/-2 <17/-2

Step 4: Simplify (Since you divided by -2, you must reverse both inequality symbols).

7/2 > x > -17/2

This is your final answer!

7/2 is greater than x and x is greater than -17/2.

Therefore, the solutions to this inequality are the numbers between -17/2 and 7/2.

I hope this helps you solve your problems!

Good luck,
Karin

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