5.


Using the inequality 4 + x ≤ 2 where x∈ℤ, fi nd the answers to the following questions.


(i) Find at least fi ve numbers that make this inequality true.


(ii) What is the largest number that makes this inequality true?


(iii) On a number line, represent, all the numbers that make this inequality true.


6. Using the inequality 3x − 5 < 4 , fi nd the answers to the following questions where x ∈ℤ.


(i) Find at least fi ve numbers that make this inequality true.


(ii) How many solutions are there in total?


(iii) What is the largest number that makes this true?


32B Taking it FURTHER


1. Write this mathematical sentence using algebra:


6 is added to a number x . Then the result is multiplied by 9. The fi nal answer is greater than 99.


2. Write this mathematical sentence using algebra:


7 is subtracted from a number y . Then the result is multiplied by 3. The fi nal answer is less than or equal to 12.


3. Write this mathematical sentence using algebra:


A number z is multiplied by 4. Then 8 is subtracted from the result. The fi nal answer is greater than or equal to 28.


4. A rectangular storage room fi ts at least 7 tables such that each have 1 square metre of surface area. The perimeter of the room is 16 m. What could the width and length of the room be?


5. Cillian has €500 in a savings account at the beginning of the summer. He wants to have at least € 200 in the account by the end of the summer. He withdraws € 25 each week for food, clothes and movie tickets.


(i) Write an inequality that represents Cillian’s situation.


(ii) For how many weeks can Cillian withdraw money from his account? Justify your answer.


6. Glenties Taxi Service charges a €2 · 20 fl at rate in addition to €0 · 65 per kilometre. Katie has no more than €10 to spend on a taxi fare.


(i) Write an inequality that represents Katie’s situation.


(ii) How many kilometres can Katie travel without exceeding her budget? Justify your answer.


7. Gerry already has €50, but needs a total of at least €250 for his holiday. He gets paid €20 per day for delivering papers. What is the least number of days he must work to get enough money for his holiday?


Now that you have completed the unit, revisit the


Something to think about …


question posed at the start of this unit.


Now try questions 2, 3 and 10 on pages 558–61


517


32 Inequalities


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