1. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Warm Up
Solve.
1. x + 6 = 13
2. 8n = 48
3. t  2 = 56
4. 6 =
x = 7
n = 6
t = 58 z 6
z = 36
Homework out to check!

2. Learn to solve and graph inequalities.

3. An inequality compares two quantities and typically uses one of these symbols:
<
is less than
is greater than  
is less than or equal to
is greater than or equal to

4. Additional Example 1: Completing an Inequality
Compare. Write < or >.
A. 23 –
>
B. 5(12)
<

5. Try This: Example 1
Compare. Write < or >.
A. 19 –
<
B. 4(15)
>

6. An inequality that contains a variable is an algebraic inequality.
A number that makes an inequality true is a solution of the inequality.
The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.

7. Word Phrase Sample Solutions
Inequality
Sample Solutions
Solution Set
x is less than 5
x < 5
x = 4
4 < 5
x = 2.1
2.1 < 5

8. Word Phrase Sample Solutions
Inequality
Sample Solutions
Solution Set
y is less than or equal to 2
y is at most 2
y  2
y = 0
0  2
y = 1.5
1.5  2
–3 –2 –

9. Solving inequalities is the same as solving an equation, but with 1 exception – when you multiply or divide by a negative #.

10. Joke of the day
A new teacher was trying to make use of her psychology courses.
She started her class by saying, "Everyone who thinks you're stupid, stand up!“
  After a few seconds, Little Johnny stood up.  The teacher said, "Do you think you're stupid, Little Johnny?" 
"No, ma'am, but I hate to see you standing there all by yourself!"

11. Solve and graph the inequality.
A. x  8
–2.5
–2.5
Subtract 2.5 from both sides.
x  5.5

12. Solve and graph the inequality.
B. 5t > 15
5t > 15
Divide both sides by 5. 5 5
t > 3

13. Solve and graph the inequality.
C. w – 1 < 8
Add 1 to both sides.
w < 9 –

14. Solve and graph the inequality.4
D. 3 
3  p 4
4 •
4 •
Multiply both sides by 4.
12  p

15. Lesson Quiz Use < or > to compare each inequality.
(2) –
Solve and graph each inequality.
3. k + 9 < 12
4. 3 
5. A school bus can hold 64 passengers. Three classes would like to use the bus for a field trip. Each class has 21 students. Write and solve an inequality to determine whether all three classes will fit on the bus.
>
>
k< 3
–5 –4–3–2– m 2
6  m
–4 –3–2–
3(21)  64; 63  64; yes ?

17. Write an equation & solve
Homework out
Warm-up
Write an equation & solve
The average weight of an elephant is 5,450 kg. This is 4,270 kg more than the average weight of a giraffe. What is the average weight of the giraffe?

18. Positive choices Respect Integrity Determination Excellence P.R.I.D.E.
Altadena
Middle
School
P.R.I.D.E. P
Positive choices R
Respect I
Integrity D
Determination E
Excellence
Monday

20. Mid-chp 1 quiz
You need 1 pieces of paper out