Writing Inequalities
Your age is
Your height is
LESS THAN
GREATER THAN
19 years.
52 inches.
a
<
19 h
>52
under
above
below
over
fewer
than
exceeds
beneath
more
than
Your speed is
There are
LESS THAN
OR EQUAL TO
GREATER THAN
OR EQUAL TO
62.
42 stinkbugs.
s
≤
62
≥
s
42
VOCABULARY
at most
at least
maximum
minimum
no more
than
no less
than
Graphing Inequalities
Graph
1. Draw a number line with 19 in
the middle.
2. Next, draw an open circle
around 19.
3. Now think: Could a = 19?
…(you should be thinking)…
* a cannot be 19 – Why?
... 19 is not less than 19.
* Since a ≠ 19, leave the
circle open.
4. Finally, draw the arrow.
“less than”
“greater than”
<––––––
––––––>
Graphing Inequalities
Graph
1. Draw a number line with 10 in the
middle.
2. 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.
4. Finally, draw the arrow.
“less than”
“greater than”
<––––––
––––––>
Graphing Inequalities
Graph
1. Draw a number line with 62 in the
middle.
2. 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
4. Finally, draw the arrow.
“less than”
“greater than”
<––––––
––––––>
Graphing Inequalities
Graph
1. Draw a number line with 42 in the
middle.
2. 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
4. Finally, draw the arrow.
“less than”
“greater than”
<––––––
––––––>
Evaluating Inequalities
1. –15 ≥ 7 – 11x
–15 ≥ 7 – 11x•3
In this inequality, could x = 3?
Rewrite the inequality, but substitute 3 for x.
–15 ≥ 7 – 33
Simplify the variable side.
–15 ≥ –26
Now, read it... is that true?
x
2.
+9<7
3
a. x = 6?
“Seven is
less than
seven?”
In this inequality, could:
x = –6?
b.
2
–2
7
ANSWER:
6 is not a possible
value for x.
“Negative
fifteen is greater
than, or equal
to, negative
26.”
11
ANSWER:
–6 is not a possible
value for x.
c.
–1
x = 30?
ANSWER:
30 is a possible
value for x.
Evaluating Inequalities
3(3) + 4 > −5
\/
9 + 4 > −5
\
/
13
> −5
Read it. Is that true?
TRUE -- x could = 3.
3(−3) + 4 > −5
\/
−9 + 4 > −5
\
/
–5
> −5
Read it. Is that true?
FALSE -- x could not = –3.
7
\/
-7
\
5
/
≤5
TRUE – x could be 7
–7
7
19
≤ 5
FALSE – x could NOT be –7
Inequalities – Multiplying w/ Negatives
Solve
1.
Look at the constant attached
to the variable.
If the number attached to
the variable is negative,
you’ve got to flip the
inequality.
2. Now, divide both sides by –9.
Inequalities – Dividing w/ Negatives
Solve
–5 •
1.
• –5
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.
2. Now, multiply both sides
by –5.
–3 •
• –3
Solving Inequalities
1.
no
flip
9 + b > –10
2.
b > –19
4.
–1 <
14 ≤ 23 + a
no
flip
3.flip –19 – x ≥ –3
–9 ≤ a
y
11
no
flip
5.
–11 < y
x ≥ –16
90 ≥ –5b
flip
–18 ≤ b
7.
no
flip
y < –72
8.
flip
z > –24
x ≤ 24
9.The product of a number and two, less than fifteen, is at least thirty–five 10.
flip
1. 5
–
y
> 12
6
6.flip
2 x
≥
x
≤ –10
3 5
no
flip
The quotient of a number and two decreased by three is no more than eleven
x
2
–
3
≤
x
≤ 28
1 1