1. Inequalities

2. Starter x < 5 ‘x is less than 5’ x ≤ 5
‘x is less than or equal to 5’ 5
x > 7
‘x is greater than 7’ 7
x ≥ 7
‘x is greater than or equal to 7’ 7

3. Inequalities Inequalities are very similar to Equations
The only difference is that you will end up with a range of values for ‘x’, rather than 1 specific value
They are solved in the same way as we did equations…

4. Inequalities
Solve the inequality below, and show the answer on a number line… ≤ 8x 32
÷ 8
÷ 8 ≤ x 4 1 2 3 4 5

5. Inequalities > >
Solve the inequality below, and show the answer on a number line…
> 3x 39
÷ 3
÷ 3
> x 13 11 12 13 14 15

6. Inequalities > > >
Solve the inequality below, and show the answer on a number line…
>
3x - 5 19
+ 5
+ 5
> 3x 24
÷ 3
÷ 3
> x 8 6 7 8 9 10

7. Inequalities
Solve the inequality below, and show the answer on a number line… ≤
6x + 6 36
- 6
- 6 ≤ 6x 30
÷ 6
÷ 6 ≤ x 5 3 4 5 6 7

8. Inequalities ≥ ≥ ≥ ≥ 5x + 3 10 - 2x 7x + 3 10 7x 7 x 1
Solve the inequality below, and show the answer on a number line… ≥
5x + 3 x
+ 2x
+ 2x ≥
7x + 3 10
- 3
- 3 ≥ 7x 7
÷ 7
÷ 7 ≥ x 1 -1 1 2 3

9. Inequalities ≤ < < ≤ 8 4x 20 2 x 5
Write down the integers that satisfy this inequality… ≤
< 8 4x 20
÷ 4
÷ 4 ≤
< 2 x 5 2 3 4 5 6
Integers (whole numbers) that satisfy this inequality are:
2, 3, 4,

10. Inequalities < < < < 3 x - 1 8 4 x 9
Write down the integers that satisfy this inequality…
<
< 3
x - 1 8
+ 1
+ 1
<
< 4 x 9 2 4 6 8 10
Integers (whole numbers) that satisfy this inequality are:
5, 6, 7, 8,

11. Inequalities
Solve the inequality below, and show the answer on a number line…
> -x 4
x by -1
x by -1 x
< -4 -6 -5 -4 -3 -2
When you multiply/divide an inequality by a negative, you must reverse the sign…

12. Inequalities
Solve the inequality below, and show the answer on a number line… ≤ x
-5x
+ 2x
+ 2x ≤ 6
-3x
÷ -3
÷ -3 ≥ -2 x
When you multiply/divide an inequality by a negative, you must reverse the sign… -4 -3 -2 -1

13. Plenary
What values of x satisfy both of these inequalities? Give your answer as a single inequality (draw a number line to show both – this will help!) 3x – 15 > 9 – 5x and 5x – 3 ≤ 25 + x

14. Summary We have learnt how to solve inequalities
We have seen that inequalities give us a range of answers
We have seen how to show these answers on a number line