year 8 maths

2J
Solving inequalities
107
PROBLEM-SOLVING AND REASONING
9, 10, 12 9, 10, 12–14
10, 11, 13–15
9 Kartik buys four cartons of milk and a $20 phone card. The total cost of his shopping was greater
than $25 .
a If c is the cost of a carton of milk, write an inequality to describe the situation above.
b Solve the inequality to find the possible values of c .
c
If the milk’s cost is a multiple of 5 cents, what is the minimum price it could be?
10 In AFL football the score is given by 6g + b, where g is the number of goals and b is the number
of behinds. A team scored 4 behinds and their score was less than or equal to 36 .
a Write an inequality to describe this situation.
b Solve the inequality.
c
Given that the number of goals must be a whole number, what is the maximum number of
goals that the team could have scored?
11 Recall that to convert degrees Celsius to degrees Fahrenheit the rule is F = 1.8C + 32 . Pippa
informs you that the temperature is between 59° and 68° Fahrenheit, inclusive.
a Solve 1.8C + 32 ≥ 59 .
b Solve 1.8C + 32 ≤ 68 .
c Hence, state the solution to 59 ≤ 1.8C + 32 ≤ 68 , giving your answer as a single inequality.
d Pippa later realises that the temperatures she gave you should have been doubled—the range
is actually 118° to 136° Fahrenheit. State the range of temperatures in degrees Celsius, giving
your answer as an inequality.
12 To say that a number x is positive is to say that x > 0 .
a If 10x − 40 is positive, find all the possible values of x . That is, solve 10x − 40 > 0 .
b Find all k values that make 2k − 6 positive.
c If 3a + 6 is negative and 10 − 2a is positive, what are the possible values of a ?
d If 5a + 10 is negative and 10a + 30 is positive, what are the possible values of a ?
13 a Prove that if 5x − 2 is positive, then x is positive.
b Prove that if 2x + 6 is positive, then x + 5 is positive.
c Is it possible that 10 − x is positive and 10 − 2x is positive but 10 − 3x is negative? Explain.
d Is it possible that 10 − x is positive and 10 − 3x is positive but 10 − 2x is negative? Explain.
14 A puzzle is given below with four clues.
Clue A: 3x > 12
Clue B: 5 − x ≤ 4
Clue C: 4x + 2 ≤ 42
Clue D: 3x + 5 < 36
a Two of the clues are unnecessary. State which two clues are not needed.
b Given that x is a whole number divisible by 4 , what is the solution to the puzzle?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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