Compound Inequalities

I.  Homework

II.  And

If we have two sets A and B, then we say that an element belongs to A and B is it belongs to both of them.  For example, s student may belong to the honor society if that student is a member of A and B where

A = the collection of all registered students

B = the collection of all student has a GPA of at least 3.0.

Your instructor cannot belong to the honor society, since he is not a student.

Example:

If

A = {x|x > -2}

B = {x|x <1}

then A and B is the in between part of the number line as will be shown in class.

Exercises:  Write the following on a number line:

A.  3x - 4 < 2 and 2x + 5 > 1

B.  5x - 2 < 3 and 4x + 7 > 3

C.  3x - 4 < 2 and 2x - 7 > 5

III.  Or

If we have two sets A and B, then we say that an element belongs to A or B is it belongs to either of them.  For example, a person can get a back seat pass to a concert if that person belongs to A or B where

A = set of people that know the band member personally.

B  = set of people that sit in the VIP seats.

We always have A and B  C A or B

Example:  If

A = {x| x < -1)

B = {x| x > 2}

then A or B are the arrows left from -1 and right from 2.

Exercises:  Sketch the solution set on a number line

A)  3x + 2 > 4 or 5x + 7 < 2

B)  x - 10 > 5  or  3x + 2 < 5

C)  4x - 2 > 2 or 5x + 1 < 11

D)  2x - 1 < 1 or 3x  + 5 > 8

IV.  Double inequalities

We can write a compound inequality as a double inequality as in the example

-3 < 2x + 5 < 7

This can be written as a compound inequality by writing

-3 < 2x + 5 and 2x + 5 < 7

Exercise:

Write the double inequality as a compound inequality and then solve it.

A.  -5 < 3x + 4 < 19

B.  2y - 1 < y + 2 < 6y + 12

C.  15 - t < t + 15 < 9t - 9

D.  h + 1 < 2/3 h < h - 2