Writing InequalitiesWriting Inequalities

Your age is Your age is

LESS THANLESS THAN1919 years. years.

Your height is

GREATER THAN

52 inches.

Your speed is Your speed is

LESS THAN LESS THAN

OR EQUAL TOOR EQUAL TO6262..

There areThere are

GREATER GREATER THAN OR THAN OR EQUAL TOEQUAL TO

42 42 stinkbugs.stinkbugs.

a<19unde

r

below

fewer than

h>52

more than

over

exceeds

no more than

maximum

at most

no less than

minimum

at least

ss 62≤ ss 42≥VOCABULARYVOCABULARY

above

beneath

Graph1. 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.

Graphing InequalitiesGraphing Inequalities

“less than” “greater than”

<––––––<–––––– ––––––>––––––>

Graph

Graphing InequalitiesGraphing Inequalities

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 InequalitiesGraphing Inequalities

Graph1. 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

circle4. Finally, draw the arrow.

“less than” “greater than”

<––––––<–––––– ––––––>––––––>

Graph

Graphing InequalitiesGraphing Inequalities1. 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?

* Since x could = 42, close the

circle

––> x is greater than or equal to 42

4. Finally, draw the arrow. “less than” “greater

than”<––––––<–––––– ––––––>––––––>

Evaluating InequalitiesEvaluating Inequalities

1. –15 ≥ 7 – 11x In this inequality, could x = 3?

Rewrite the inequality, but substitute 3 for x.

–15 ≥ 7 – 11x

•3

Simplify the variable side.–15 ≥ 7 – 33–15 ≥ –26

“Negative fifteen is greater than, or equal to, negative

26.”Now, read it...is that

true?2. + 9 < 7 In this inequality, could:

a. xx = 6 = 6? b. xx = –6 = –6? c. xx = 30 = 30?3x

–2

7

“Seven is less than seven?”

ANSWER:6 is notnot a possible

value for x. 11

ANSWER:–6 is notnot a possible

value for x.

–1 ANSWER:30 isis a possible

value for x.

2

Evaluating InequalitiesEvaluating 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 ≤ 5FALSE – x could NOT be –7

Inequalities – Multiplying w/ Inequalities – Multiplying w/ NegativesNegatives

Solve

1. Look at the constant attached to the variable.

2. Now, divide both sides by –9.

If the number attached to the variable is

negative, you’ve got to flip the inequality.

1. Look at the constant attached to the variable.

• –5–5 •

2. Now, multiply both sides by –5.

If the number attached to the variable is

negative, you’ve got to flip the inequality.

Solve

• –3–3 •

Inequalities – Dividing w/ Inequalities – Dividing w/ NegativesNegatives

Is it negative?

Solving InequalitiesSolving Inequalities

1. 9 + b > –10 2. 14 ≤ 23 + a 3. –19 – x ≥ –3

4. –1 < 5. 90 ≥ –5b 6. > 12

7. 8.

9.The product of a number and two, less than fifteen, is at least thirty–five 10. The quotient of a number and two decreased by three

is no more than eleven

.

11

y

6y

no flip

–9 ≤ a

x ≥ –16

b > –19

no flip

flip

no flip

flip flip

no flip

flip

–11 < y

–18 ≤ b

y < –72

x ≤ 24

z > –24

15 – 2x ≥ 35 x – 3 ≤ 11 2

x ≤ –10 x ≤ 28

flip no flip