1. GCSE: Inequalities – Shading Regions
Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx
GCSE: Inequalities – Shading Regions
Dr J Frost } ~
Last modified: 31st August 2015

2. RECAP: Inequalities on a Number Line
This is known as a ‘strict’ inequality.
x > 3
x < -1
Means: x is (strictly) greater than 3. ?
Means: x is (strictly) less than -1. ? ? ?
x ≥ 4
x ≤ 5
Means: x is greater than or equal to 4. ?
Means: x is less than or equal to 4. ? ? ?

3. STARTER: Solving Inequalities
(On your worksheet) ?
−𝟐,−𝟏,𝟎,𝟏,𝟐,𝟑
𝒙<𝟒 ? ?
𝒙<−𝟒 ?
𝟔<𝒙≤𝟗

4. Sketch the region representing 𝑥>2 8 6 4 2 -2 -4 -6
Sketch the region representing 𝑥>2
Think: How are the values of x constrained, and how are the values of y constrained?
Get students to sketch axes and tables in their books.
𝒙 can be any number greater than 2, but 𝒚 can be ANY value because it is not constrained.
The dotted line indicates that 𝒙 can’t be 2.

5. 8 6 4 2 -2 -4 -6
-4 < y ≤ -2
Get students to sketch axes and tables in their books.

6. y ≥ x How can we tell which way round the inequality is? 8 6 4 2 -2 -4 -6
y ≥ x
Get students to sketch axes and tables in their books.
How can we tell which way round the inequality is?
Just try a point on one side, e.g. (0, 4). Is y ≥ x? Yes, so we’re on the right side.

7. Quickfire Regions             Fail Win Fail Win Fail
Bro Tip: An easier way to see if the region is on the correct side is to see whether 𝑦 is on the smaller side of the inequality or the greater side. If the greater, we’re above.
Is the region on the correct side of the line?
y > x + 2
y – x > 1
y > 1 - x 2 1 1
Fail 
Win 
Fail  
Win
Fail 
Win 
x > 2y - 3
y > -x
x + y > 1
1.5 1 
Fail
Win 
Fail  
Win 
Fail 
Win

8. y ≤ x + 1 and x ≤ 6 and y > 2 Combining Inequalities 8 6 4 2 -2 -4 8 6 4 2 -2 -4 -6
Combining Inequalities
y ≤ x + 1 and x ≤ 6 and y > 2
Get students to sketch axes and tables in their books.
Bro Tip: In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines.

9. Question 4
Worksheet Answers
Click to Sketch >    

10. Question 5
Worksheet Answers   
Click to Sketch >

11. Question 6 ? Worksheet Answers Click to Sketch > R
𝟐,𝟐 , 𝟐,𝟑 , 𝟐,𝟒 , (𝟑,𝟑) ?

12. Question 7
Worksheet Answers      
Click to Sketch >

13. Question 8
Worksheet Answers
Click to Sketch >     ? 3 ? 2

14. R Question 9 ? ? ? Worksheet Answers 𝟓 𝟐 − 𝟓 𝟔 𝒙 𝟐𝟎
Click to Sketch > ?