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Starter
x < 5
‘x is less than 5’
x ≤ 5
‘x is less than or equal to 5’
5
5
x > 7
‘x is greater than 7’
7
x ≥ 7
‘x is greater than or equal to 7’
7
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…
Inequalities
• Solve the inequality below, and show the
answer on a number line…
÷8
1
8x
≤
32
x
≤
4
2
3
4
÷8
5
Inequalities
• Solve the inequality below, and show the
answer on a number line…
÷3
11
3x
>
39
x
>
13
13
14
12
÷3
15
Inequalities
• Solve the inequality below, and show the
answer on a number line…
+5
3x - 5
>
19
3x
>
24
÷3
x
6
7
>
8
8
9
+5
÷
3
10
Inequalities
• Solve the inequality below, and show the
answer on a number line…
-6
6x + 6
≤
36
6x
≤
30
÷6
x
3
4
≤
5
5
6
-6
÷
7
6
Inequalities
• Solve the inequality below, and show the answer on a
number line…
+ 2x
-3
5x + 3
≥
10 - 2x
7x + 3
≥
10
7x
≥
7
≥
1
÷7
x
-1
0
1
2
+ 2x
-3
÷7
3
Inequalities
• Write down the integers that satisfy this inequality…
÷4
2
8
≤
4x
2
≤
x
3
4
<
<
5
20
÷4
5
6
Integers (whole numbers) that satisfy this inequality are:
2, 3, 4,
Inequalities
• Write down the integers that satisfy this inequality…
<
<
3
+1
4
2
4
x-1
x
6
<
<
8
8
+1
9
10
Integers (whole numbers) that satisfy this inequality are:
5, 6, 7, 8,
Inequalities
• Solve the inequality below, and show the
answer on a number line…
x by -1
-6
-5
-x
>
x
< -4
-4
4
-3
x by -1
-2
When you
multiply/divide an
inequality by a negative,
you must reverse the
sign…
Inequalities
• Solve the inequality below, and show the
answer on a number line…
+ 2x
6 - 2x
≤
-5x
6
≤
-3x
÷ -3
-2
-4
-3
≥
-2
x
-1
+ 2x
÷
-3
When you
multiply/divide an
inequality by a negative,
you must reverse the
0
sign…
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
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