1. Do Now 3/5/14 Take out HW from last night. Text p. 463, #2-36 evens
Copy HW in your planner.
Practice worksheet 11.4 B
In your notebook, answer the following question. Outside of the math classroom, where have you heard phrases such as “at least” or “no more than”? Give examples. How would you write the phrases mathematically?

2. Homework Text p. 463, #2-36 evens
2) isolate the variable
4) proportion
6) -81
8) 12
10) 7/6 or 1 1/6
12) 7/99
14) -9
16) 8
18) 25
20) -47
22) 5
24) -0.75
26) 26
28) 1/8
30) 4.5
32) 87.5
34) 5
36) 45

3. Objective
SWBAT read and write inequalities and graph them on a number line

4. Section 11.4, “Inequalities”
mathematical sentence formed by placing a <, ≤, >, or ≥ between two expressions.
13 ≥ 14 - z
y – 8 < 12
x +8 > 30
11 + a ≤ 121

5. < ≤ > Writing Inequalities Fewer than, below Is less than
Symbol
Meaning
Key Phrase
Is less than
Fewer than, below
<
At most, no more than ≤
Is less or equal to
More than, above
Is greater than
>
Is greater than or equal to
At least, no less than

6. On a number line, the GRAPH OF AN INEQUALITY is the set of points that represent the SOLUTION SET of the inequality.
“Less than” and “greater
than” are represented
with an open circle.
x < 8 5 6 7 8 9 10 11
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
x ≥ 11 8 9 10 11 12 13 14

7. Graph each inequality x < -3 x ≥ 7 -6 -5 -4 -3 -2 -1 4 5 6 7 8 9 10
“Less than” and “greater
than” are represented
with an open circle. -6 -5 -4 -3 -2 -1
x ≥ 7
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle. 4 5 6 7 8 9 10

8. Graph each inequality 7 ≥ y -1 < h 4 5 6 7 8 9 10 -4 -3 -2 -1 1 2
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle. 4 5 6 7 8 9 10
-1 < h
“Less than” and “greater
than” are represented
with an open circle. -4 -3 -2 -1 1 2

9. Write an inequality represented by the graph.
SOLUTION
The closed circle means that 8 is not a solution of the inequality. Because the arrow points to the left, all numbers less than 8 are solutions.
ANSWER
An inequality represented by the graph is x < 8.

10. Write an inequality represented by the graph.
SOLUTION
The closed circle means that – 2.5 is a solution of the inequality. Because the arrow points to the right, all numbers greater than – 2.5 are solutions.
ANSWER
An inequality represented by the graph is x > – 2.5.

11. The highest temperature recorded in the United States was 134°F at Death Valley, California, in Use only this fact to write and graph an inequality that describes the temperatures in the United States.
SOLUTION
Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134.

12. COMPOUND INEQUALITY –
consists of two separate inequalities joined by AND or OR.

13. “AND” Compound Inequalities
The graph of a compound inequality with AND is the INTERSECTION of the graphs of the inequalities.
Graph x > -2 -2 -1 1 2 3
Graph x ≤ 1 -2 -1 1 2 3
Graph of x ≤ 1 and x > -2
Graph -2< x ≤ 1 -2 -1 1 2 3

14. “OR” Compound Inequalities
The graph of a compound inequality with OR is the UNION of the graphs of the inequalities.
Graph x > 2 -2 -1 1 2 3
Graph x ≤ -1 -2 -1 1 2 3
Graph of x ≤ -1 or x > 2 -2 -1 1 2 3

15. Graph each compound inequality4 5 6 7 8 9 10
h > 1 or h ≤ -3 -4 -3 -2 -1 1 2

16. Graph each compound inequality
y ≤ 16 or y > 20 14 15 16 17 18 19 20
h > -3 and h ≤ 0 -4 -3 -2 -1 1 2

17. Translate the verbal phrase into an inequality. Then
Challenge
Translate the verbal phrase into an inequality. Then
graph the inequality.
All real numbers that are greater than – 2 and less
than 3.
Inequality:
– 2 < x < 3
Graph:
All real numbers that are less than 0 or greater than
or equal to 2.
Inequality:
x < 0 or x ≥ 2
Graph:

18. Practice worksheets 11.4 B & C
Homework
Practice worksheets 11.4 B & C