The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

Positive vs. Negative”

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

A quantity x is positive means that x is more than 0, i.e. 0 < x,

Positive vs. Negative”

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

A quantity x is positive means that x is more than 0, i.e. 0 < x,

0

+ x is positive

Positive vs. Negative”

On the real line:

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

A quantity x is positive means that x is more than 0, i.e. 0 < x, and that x is negative means that x is less than 0, i.e. x < 0.

0

+– x is negative x is positive

Positive vs. Negative”

On the real line:

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

A quantity x is positive means that x is more than 0, i.e. 0 < x, and that x is negative means that x is less than 0, i.e. x < 0.

0

+– x is negative x is positive

Hence “the temperature T is positive” is translated as “0 < T”.

“the account balance A is negative”, is translated as “A < 0”.

Positive vs. Negative”

On the real line:

Inequalities and Comparative Phrases

The following adjectives or comparison phrases may be translated into inequalities:“positive”↔“negative”,“non–positive”↔”non–negative”,“more/greater than”↔ “less/smaller than”,“no more/greater than”↔ “no less/smaller than”, “ at least” ↔”at most”,

Inequalities II

A quantity x is positive means that x is more than 0, i.e. 0 < x, and that x is negative means that x is less than 0, i.e. x < 0.

0

+– x is negative x is positive

Hence “the temperature T is positive” is translated as “0 < T”.

“the account balance A is negative”, is translated as “A < 0”.

Positive vs. Negative”

On the real line:

Inequalities and Comparative Phrases

Inequalities and Comparative PhrasesNon–Positive vs. Non–Negative

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

Non–Positive vs. Non–NegativeInequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Non–Positive vs. Non–Negative

On the real line:

Inequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Hence “the temperature T is non–positive” is “T ≤ 0”.“the account balance A is non–negative” is “0 ≤ A”.

Non–Positive vs. Non–Negative

On the real line:

Inequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Hence “the temperature T is non–positive” is “T ≤ 0”.“the account balance A is non–negative” is “0 ≤ A”.

Non–Positive vs. Non–Negative

On the real line:

“More/greater than” vs “Less/smaller than”

Inequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Hence “the temperature T is non–positive” is “T ≤ 0”.“the account balance A is non–negative” is “0 ≤ A”.

Non–Positive vs. Non–Negative

On the real line:

“More/greater than” vs “Less/smaller than”Let C be a number, x is greater than C means “C < x”, and that x is less than C means “x < C”.

Inequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Hence “the temperature T is non–positive” is “T ≤ 0”.“the account balance A is non–negative” is “0 ≤ A”.

Non–Positive vs. Non–Negative

On the real line:

“More/greater than” vs “Less/smaller than”Let C be a number, x is greater than C means “C < x”, and that x is less than C means “x < C”.

C x is less than C

x is more than COn the real line:

Inequalities and Comparative Phrases

A quantity x is non–positive means x is not positive, or “x ≤ 0”, and that x is non–negative means x is not negative, or “0 ≤ x”,

0

+

– x is non–positive

x is non–negative

Hence “the temperature T is non–positive” is “T ≤ 0”.“the account balance A is non–negative” is “0 ≤ A”.

Non–Positive vs. Non–Negative

On the real line:

“More/greater than” vs “Less/smaller than”Let C be a number, x is greater than C means “C < x”, and that x is less than C means “x < C”.

C x is less than C

x is more than C

Hence “the temperature T is more than –5 ” is “–5 < T”.“the account balance A is less than 1,000” is “A < 1,000”.

On the real line:

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

0

+

– x is no more than C

x is no less than COn the real line:C

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

0

+

– x is no more than C

x is no less than C

“The temperature T is no–more than 250o” is “T ≤ 250”.“The account balance A is no–less than 500” is “500 ≤ A”.

On the real line:C

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

0

+

– x is no more than C

x is no less than C

“The temperature T is no–more than 250o” is “T ≤ 250”.“The account balance A is no–less than 500” is “500 ≤ A”.

On the real line:C

“At least” vs “At most”“At least C” is the same as “no less than C” and“at most C” means “no more than C”.

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

0

+

– x is no more than C

x is no less than C

“The temperature T is no–more than 250o” is “T ≤ 250”.“The account balance A is no–less than 500” is “500 ≤ A”.

On the real line:C

“At least” vs “At most”“At least C” is the same as “no less than C” and“at most C” means “no more than C”.

0

+

– x is at most C

x is at least COn the real line:C

Inequalities and Comparative Phrases

“ No more/greater than” vs “No less/smaller than”A quantity x is no more greater than C means “x ≤ C”, and that x is no–less than C means “C ≤ x”,

0

+

– x is no more than C

x is no less than C

“The temperature T is no–more than 250o” is “T ≤ 250”.“The account balance A is no–less than 500” is “500 ≤ A”.

On the real line:C

“At least” vs “At most”“At least C” is the same as “no less than C” and“at most C” means “no more than C”.

0

+

– x is at most C

x is at least C

“The temperature T is at least 250o” is “250o ≤ T”.

“The account balance A is at most than 500” is “A ≤ 500”.

On the real line:C

Inequalities and Comparative Phrases

Exercise. A. Draw the following Inequalities. Translate each inequality into an English phrase. (There might be more than one ways to do it)1. x < 3 2. –5 ≤ x 3. x < –8 4. x ≤ 12 5. x ≥ 3 6. –5 > x 7. x ≥ –8 8. x > 12 Exercise. B. Translate each English phrase into an inequality. Draw the Inequalities.Let P be the number of people on a bus.9. There were at least 50 people on the bus.10. There were no more than 50 people on the bus.11. There were less than 30 people on the bus.12. There were no less than 28 people on the bus.Let T be temperature outside.13. The temperature is no more than –2o.14. The temperature is at least than 35o.15. The temperature is positive.

Inequalities and Comparative Phrases

Let M be the amount of money I have.16. I have at most $25.17. I have non–positive amount of money.18. I have less than $45.19. I have at least $250.

Let the basement floor number be given as negative number and that F be floor number that we are on.20. We are below the 7th floor.21. We are above the first floor.22. We are not below the 3rd floor basement.24. We are on at least the 45th floor.25. We are between the 4th floor basement and the 10th floor.26. We are in the basement.

Inequalities and Comparative Phrases