Ch. 3.5 Compound InequalitiesCompound inequality: are two inequalities that are joined by the word AND or the word OR

1. Writing a compound inequalityex 1: all real numbers that are at least -2 and at most 4N ≥ -2 and n ≤ 4-2 ≤ n ≤ 4

ex 2: Today’s temperatures will be above 32ᵒF, but not as high as 40ᵒF.

32 < t and t < 40 32 < t < 40

ex 3: all real numbers greater than -2 but less than

32 40

Practice

1. All real numbers that are at least 2 and at most 9

2. All real numbers that are between -3 and 8

Solving a compound inequality containing ANDex:Solve -4 < r – 5 ≤ -1. Graph your solution

Write the compound inequality as two inequalities joined by and.

-4 < r – 5 and r – 5 ≤ -1+5 +5 + 5 + 5

1 < r and r ≤ 4

Solving a Compound Inequality Containing AND

Ex 2:Solve -6 ≤ 3x < 15

Write my two inequalities

-6 ≤ 3x and 3x < 15 3 3 3 3

-2 ≤ x and x < 3

-2 ≤ x < 3

Practice

1. -3 < 2x – 1 < 7

Practice

1. 7 < -3n + 1 ≤ 13

Solving inequalities in word problems

The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8, all together. The first two readings for a swimming pool are 7.4 and 7.9. What are possible values for the third reading p will make the average pH normal?

How do I find average?Where does my average have to be inbetween?

7.2 ≤ ( 7.4 + 7.9 + p) ≤ 7.8 3

21.6 ≤ 7.4 + 7.9 + p ≤ 23.4

21.6 ≤ 15.3 + p ≤ 23.4

I first need to get 3 out of the denominator in order to get p all by itself!

(3) (3) (3)

21.6 ≤ 15.3 + p ≤ 23.4

Break into two inequalities

21. 6 8 ≤ 15.3 + p and 15.3 + p ≤ 23.4- 15.3 - 15.3 - 15.3 -15.3

6.3 ≤ p and p ≤ 8.1

Practice

Suppose the first two readings for the acidity of the water in a swimming pool are 7.0 and 7.9. What possible values for the third reading will make the average pH normal?

Homework

Pages 163-164 #’s 1-19

POW DUE TOMORROW!!!!!!!!!!