Linear Inequalities


Calculators are allowed for all questions unless indicated by the question. There are 5 questions for this topic. The difficulty increases with the question number.

Question 1: (Non-calculator)

A. State 3 integers that satisfy the following inequality: $x -2 < 0$ (2 marks)

B. Calculate the range of values of $x$ (1 mark)

$x-2$ must be smaller than 0.

Some possible integers include 1, -1, -2, -3 etc… (2 marks)

$x-2 < 0$

$x < 2$ (1 mark)

Question 2: (Non-calculator)

A. State 3 integers that satisfy the following inequality: $3x +2 > 8$ (2 marks)

B. Calculate the range of values of $x$ (2 marks)

since $3x +2$ must be larger than 8, possible integers include 3,4,5 etc..

Do not accept 2, as the it must be greater than 8, not greater than or equal to. (2 marks)

$3x + 2 > 8$

$3x > 6$ (1 mark)

$x > 2$ (divide by 3) (1 mark)

Question 3: (Non-calculator)

A. State all the possible integers in the following inequality: $-2 \leq x \leq 4$ (2 marks)

B. Draw a number line to represent this inequality (2 marks)

$x$ must be larger than or equal to $-2$, and smaller than or equal to $4$.

All the possible integers are -2,-1, 0, 1, 2, 3 ,4 (2 marks)

Award 2 marks for correct number line, allow 1 mark if hollow circle used.

Question 4: (Non-calculator)

Solve the following inequality:

$2x +3 \geq x-4$ (2 marks)

$2x+3 \geq x-4$

$x +3 \geq -4$ (1 mark)

$x \geq -7$ (1 mark)

Question 5: (Non-calculator)

Solve the following inequality giving your answer in set notation

$4(x+3) \leq 3x + 4$ (3 marks)

$4x + 7 \leq 3x + 4$

$x +7 \leq 4$ (1 mark)

$x \leq -3 $ (1 mark)

= $ {x: x\leq -3} $ (1 mark)