7. Diarmuid has a €30 online gift voucher. He plans to buy as many books as he can. The cost of each book is €4 . There is also a single shipping charge of €2.
(i) Write an inequality to represent Diarmuid’s situation.
(ii) Use your answers from part (i) to fi nd the maximum number of books Diarmuid can aff ord without spending more than his gift voucher amount.
8. Oisín is y years old. Michael is 9 years younger than Oisín. The sum of their ages is less than 41. (i) Write down in terms of y , an inequality to show this information.
(ii) Work out the oldest age that Oisín can be. Give your answer as a whole number of years.
9. Ann, Mary and Angela go shopping. Ann spends m euros. Mary spends twice as much as Ann. Angela spends 5 euros more than Ann. The total amount of money spent, in euros, is more than €60.
(i) Write down, in terms of m , an inequality to show this information.
(ii) Each girl spends a whole number of euros. Work out the least each girl could have spent.
Revision questions
32A Core skills 1. Represent the following inequalities on a number line.
(i) x < 3 where x ∈ℤ (ii) x > − 6 where x ∈ℝ (iii) x > − 5 where x ∈ ℕ (iv) x < 3 where x ∈ ℕ (v) x ≤ 2 where x ∈ℤ (vi) x > − 4 where x ∈ℤ
2. Solve the following inequalities and show the solution on a number line.
(i) x + 5 > 12 where x ∈ ℕ (ii) 3x − 7 < 5 where x ∈ℝ (iii) 3b + 2 > 8 where b ∈ℝ
3. Using the numbers in red below each inequality, decide which of the values for x satisfy each inequality ( x ∈ℝ ).
(i) 9 ( 2 + 3x) < 72 1 3 − 1 4
(ii) 2(3x − 2) > − 52 − 10 − 6 − 8 − 9
(iii) 4 (2x + 5) < − 44 10 − 8 − 9 − 10
4. Solve the following inequalities and show the solution on a number line.
(i) 3 ( 6x + 2 ) < 42 where x ∈ℤ (ii) 8 ( 1 + 2b) < 40 where b ∈ℝ (iii) 8x + 4 < 12 where x ∈ℝ (iv) 5y − 2 > 8 where y ∈ℤ