Compound Inequalities

Question

Definition Words

◦Compound inequalities

◦And

◦Or

◦Intersection

◦Union



1). 12 < 12 + 4x < 0

2). 12 – x > 15 or 7x – 13 > 1

I divide it up the compound inequalities into two problems

12 <12+ 4x

4 x >0

or

x >0

and

12+4x <0

4 x < -12

x < - 3

so x is either left of -3 or right of 0 on a number line

12 - x > 15

-x > 3

I then multiplied both sides by -1 and changed the direction of the arrow when I changed the signs.

x < - 3



7 x - 13 > 1

7 x > 14

x > 2



so x is left of -3 or right of +2

I need someone to check and see if this is correct and how do I use the vocabulary words correctly. I'm having a difficult time with this.

Answer 1

There is no solution to #1 since 12 is not less than 0.
As written
12 < 12 + 4x < 0
means 12 < 12+4x AND 12+4x < 0
To find such a number, you would need
12 < 0

12 – x > 15 or 7x – 13 > 1

12-x > 15
-3 > x

7x-13 > 1
7x > 14
x > 2

You are correct