**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)

Answer to part A

$x-2$ must be smaller than 0.

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

Answer to part B

$x-2 < 0$

$x < 2$ (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)

Answer to part A

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)

Answer to part B

$3x + 2 > 8$

$3x > 6$ (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)

Answer to part A

$x$ 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)

Answer to part B

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)

Answer to part A

$2x+3 \geq x-4$

$x +3 \geq -4$ (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)

Answer to part A

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

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

$x \leq -3 $ (1 mark)

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