1. GREATER THAN OR EQUAL TO
Writing Inequalities
Your speed is
LESS THAN
OR EQUAL TO
62.
There are
GREATER THAN OR EQUAL TO
42 stinkbugs.
Your age is
LESS THAN
19 years.
Your height is
GREATER THAN
52 inches.
>
< ≤ ≥ a s 19 h 52 62 s 42
above
under
VOCABULARY
over
below
at most
at least
exceeds
fewer than
maximum
minimum
more than
beneath
no more than
no less than

2. Graphing Inequalities
Inequalities, p.4
Graphing Inequalities
Draw a number line with 19 in
the middle.
Graph
Next, draw an open circle
around 19.
3. Now think: Could a = 19?
…(you should be thinking)…
* a cannot be 19 – Why?
is not less than 19.
* Since a ≠ 19, leave the
circle open.
Finally, draw the arrow.
“less than” “greater than”
<–––––– ––––––>
Inequalities, p.4

3. Graphing Inequalities
Inequalities, p.4
Graphing Inequalities
Draw a number line with 10 in the
middle.
Graph
Next, draw an open circle around
10.
3. Now think: Could x = 10?
…(you should be thinking)…
* x cannot be 10 – Why?
10 is not greater than 10.
* Since x ≠ 10, leave the
circle open.
Finally, draw the arrow.
“less than” “greater than”
<–––––– ––––––>
Inequalities, p.4

4. Graphing Inequalities
Draw a number line with 62 in the
middle.
Graph
Next, draw an open circle around
62.
3. Now think: Could s = 62?
* s can be 62 – Why?
––> s is less than or equal to 62
* Since s could = 62, close the
circle
Finally, draw the arrow.
“less than” “greater than”
<–––––– ––––––>

5. Graphing Inequalities
Draw a number line with 42 in the
middle.
Graph
Next, draw an open circle around
42.
3. Now think: Could x = 42?
* x can be 42 – Why?
––> x is greater than or equal to 42
* Since x could = 42, close the
circle
Finally, draw the arrow.
“less than” “greater than”
<–––––– ––––––>

6. •3 Evaluating Inequalities 1. –15 ≥ 7 – 11x 2. + 9 < 7
Inequalities, p.4
Evaluating Inequalities
1. –15 ≥ 7 – 11x
In this inequality, could x = 3?
–15 ≥ 7 – 11x •3
Rewrite the inequality, but substitute 3 for x.
“Negative fifteen is greater than, or equal to, negative 26.”
–15 ≥ 7 – 33
Simplify the variable side.
–15 ≥ –26
Now, read it...
is that true?
< 7
In this inequality, could:
a. x = 6? b. x = –6? c. x = 30?
“Seven is less than seven?” 2 –2
ANSWER:
6 is not a possible value for x.
ANSWER:
–6 is not a possible value for x. –1
ANSWER:
30 is a possible value for x. 11 7
Inequalities, p.4

7. Evaluating Inequalities
3(3) > −5
\ /
> −5
\ /
> −5
Read it. Is that true?
TRUE -- x could = 3. 7 \/
- 7
\ /
≤ 5
TRUE – x could be 7 –7
3(−3) > −5
\ /
− > −5
\ /
– > −5
Read it. Is that true?
FALSE -- x could not = –3. 7
≤ 5
FALSE – x could NOT be –7

8. Inequalities – Multiplying w/ Negatives
Solve
Look at the constant attached
to the variable.
If the number attached to the variable is negative, you’ve got to flip the inequality.
Now, divide both sides by –9.

9. Inequalities – Dividing w/ Negatives
Solve
–5 •
• –5
–3 •
• –3
Look at the constant attached
to the variable.
Is it negative?
If the number attached to the variable is negative, you’ve got to flip the inequality.
Now, multiply both sides by –5.

10. Solving Inequalities 1. 9 + b > –10 2. 14 ≤ 23 + a 3. –19 – x ≥ –38.
9.The product of a number and two, less than fifteen, is at least thirty–five The quotient of a number and two decreased by three is no more than eleven .
no flip
no flip
flip
b > –19
–9 ≤ a
x ≥ –16
no flip
flip
flip
–11 < y
–18 ≤ b
y < –72
no flip
flip
x ≤ 24
z > –24
x – 3 ≤ 11 2
flip
15 – 2x ≥ 35
no flip
x ≤ –10
x ≤ 28