Expert: Pawan Musale - 9/21/2009

Question
give answer in interval notation
12<-4x+4 less than or equal to 28

Answer
Hi Jennifer,

Given equation is:

12 < -4x+4 <= 28

This is double inequality and hence we will split it into two inequalities:

12 < -4x+4 --------------------- #1
-4x+4 <=28 --------------------- #2

Let us solve first inequality:

12 < -4x+4

8 < -4x
2 < -x

Dividing both sides by -1 (inequality sign gets reversed when multiplying or dividing by negative number)

-2 > x ------------------------ #3

Let us solve second inequality:

-4x+4 <=28
-4x <= 24
Dividing both sides by -4,
x >= -6 ---------------------#4 (notice inequality sign reversed due to division by begative number)

From results #3 and #4 above, we get value of x as

-2 > x >= -6

Rewriting,

-6 =< x < -2

Means x is either equal to or greater than -6 but less than -2.

Hence interval notation for this inequality is [-6, -2). This is your answer.

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Some additional information about interval notations can be found on:

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotatio...

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I believe this helps you.

Let me know if you need additional information.

Regards,
Pawan