INEQUALITIES
Higher Tier
INEQUALITIES – COMPARING NUMBERS The symbol „>‟ stands for “is greater than” The symbol „ 3. 3 is less than 7 can be writte...
DOUBLE INEQUALITIES Suppose that in order to run a trip, the number of pupils going must be at least 12 and not more than 45. Taking x as the number of pupils going, the number of pupils going can be 12 or more, so x 12, or 12 x and the number of pupils can be 45 or less, so x 45. Combining both of these conditions, we can write:
12 x 45
Example The number of matches in a box varies. Taking this number as x, we are told that 30 < x 36. This means that
30 < x and x 36
in words, there are more than 30 matches in the box and there are not more than 36 matches in the box.
INEQUALITY WITH EQUALITY Miss Evans will organise a trip to the theatre provided that at least 15 pupils want to go. This means that the number of pupils can be exactly 15 or any number greater than 15. If x pupils want to go, the trip can take place if x = 15 or x > 15 We can combine these two conditions and write: x 15.
Example 1 The minimum number of days for which a holiday cottage can be booked is 7. If x is the number of days, we can write x 7. Example 2 A theatre is licensed to seat 600 people. If x is the number of tickets sold for a performance then we can write x 600.
EXERCSIE In each question use or to write a statement for x. 1.
The Basketball club will accept applications for members only from players who are at least 6 feet tall. Take x feet as the height of a successful applicant.
2.
A notice at the Pleasure Cruise ticket office states that the maximum number of passengers is 50. Take x as the number of passengers.
3.
At the local petrol station the pumps will not dispense less than 5 litres of petrol. I buy x litres.
4.
Correctly mixed antifreeze protects a car engine at temperatures down to 5oC. My engine is protected when the temperature is x oC.
5.
A maximum of six standing passengers are permitted on a bus. The conductor allows x people to stand.
“ ” We don‟t know exactly what the temperature will be, so call it x. We can now write x > 4. This is an inequality and it is true when x is any number greater than 4 but not including 4.
Numbers satisfying an inequalities can be found.
Example 1 Write down any whole number that satisfies the inequality x < 4. Solution Any number that is on the left of 4 on the number line such as 1 or 2 or 3 etc. Example 2 Write down the biggest whole number that satisfies the inequality x < 4. Solution 3 Example 3 Write down the smallest whole number that satisfies the inequality x > 2. Solution 1 Notice that x > 4 means the same as 4 < x
The temperature tonight will be below freezing. If the temperature tonight is x o C, write an inequality for x.
2.
I have to keep more than £20 in my bank account. If I have £x in my account at the moment, write an inequality for x.
3.
To earn a bonus, John has to assemble more than 34 fan heaters in a day. Yesterday John assembled x fan heaters and earned a bonus. Write an inequality for x.
4.
Give the smallest whole number that satisfies the given inequality
5.
a.
x > 12
b.
x > 4
c.
x>0
d.
x > 9
Give the largest whole number that satisfies the given inequality a.
x 36.
8.
Give the largest whole number that is exactly divisible by 3 and 5 and which satisfies the inequality x < 40.
