1. Inequalities and Inequations
Mathematics
Inequalities and Inequations

2. Aims of the Lesson The aim of this powerpoint is to help you…
learn the symbols for inequalities
represent inequalities on number lines
solve simple inequations

3. Inequalities Inequalities can be represented in written form
using a number-line diagram
using shaded region(s) on a graph

4. Written Inequalities SYMBOLS: > means greater than
< means smaller than
 means greater than or equal to
 means smaller than or equal to
REMEMBER:
Either the point end of the sign points to the
smaller number OR the bigger end is a crocodile’s
open mouth which wants to eat the bigger number.

5. Examples of Written Inequalities
5 > 1 5 is greater than 1
7 < is smaller than 25
2 < n < 5 n is any value between 2 and 5
(not including 2 or 5)
– 3  b < 0 b is any value between – 3 and
0, it can include – 3 but not 0

6. Inequality Notation for Number Lines
A value represented by a circle is a limit
If the circle is coloured in, the limit is included in the equality (i.e. use  or )
If the circle is left empty, the limit is not included in the inequality (i.e. use < or >)
All values represented by a line are included

7. Number Line Examples Represent: n > 5 (Red line)
n>5 means n is bigger than 5, so the line is on the side where the numbers are bigger than 5 and the limit is at 5
Represent: 3 < n  6 (Green line)
This means n is between 3 (not included so empty circle) and 6 (can equal this so coloured in circle) –

8. Solving Inequations
Imagine there is a = sign instead of the inequality symbol
Use the balancing method to solve the inequality
BUT
If you multiply or divide both sides by a negative number, invert the inequality symbol

9. Examples Solve: Y – 2 < 13 (+2) Y < 15 (ANSWER)
Solve: 3x + 7 > 5 – x
(+x) 4x + 7 > 5
(-7) 4x > – 2
(÷4) x > – ½ (ANSWER)

10. What next?
Make appropriate notes (including examples) on collecting like terms or printout the prepared notes and complete all the tasks within them.
Work through the MyMaths lessons (and then their online homeworks) called:
Algebra > Inequalities > Inequalities and Intervals
Algebra > Inequalities > Inequations
Save and complete the worksheets:
InEq-S1.xlsx and InEq-S3.xlsx