Page 133 - Cambridge+Checkpoint+Mathematics+Coursebook+9

13.6 Inequalities

13.6 Inequalities

Here is an equation: 2x + 3 = 10

To solve it, 'rst subtract 3. 2x = 7

!en divide by 2. x = 3.5
Now here is an inequality. 2x + 3 < 10 Remember: < means ‘less than’.
You can solve an inequality in the same way as an equation.
First subtract 3. 2x < 7

!en divide by 2. x < 3.5

!e solution set is any value of x less than 3.5. You can show this
on a number line.
< less than
–3 –2 –1 0 1 2 3 4 5 6 > more than

!e open circle ( n) shows that 3.5 is not included. ≤ less than or equal to
You need to know the four inequality signs in the box. ≥ more than or equal to

Worked example 13.6

The perimeter of this triangle is at least 50 cm.
a Write an inequality to show this. x cm
b Solve the inequality. x + 2 cm
c Show the solution set on a number line.
x + 3 cm

a 3x + 5 ≥ 50 ‘At least 50’ means ‘50 or more’.
b 3x ≥ 45 Subtract 5 from both sides.
x ≥ 15 Divide both sides by 3.
C The closed circle ( n) shows that 15 is in the solution set.
–15 –10 –5 0 5 10 15 20 25 30

) Exercise 13.6 –4 –3 –2 –1 0 1 2 3 4

–4
1 Write down an inequality to describe each of these solution sets. –2 –1 0 1 2 3 4
–3
a –4 –3 –2 –1 0 1 2 3 4 b –6 –4 –2 0 2 4 6 8
–4 –3 –2 –1 0 1 2 3 4 –6 –4 –2 0 2 4 6 8
–6 –4 –2 0 2 4 6 8 –20 –15 –10 –5 0 5 10 15 20
c d
–6 –4 –2 0 2 4 6 8 –20 –15 –10 –5 0 5 10 15 20
–20 –15 –10 –5 0 5 10 15 20 –40 –30 –20 –10 0 10 20 30 40
10
5
20
15
–5
–20 –15 –10
0
2 Show each of these solution sets on a number line. –40 –30 –20 –10 0 10 20 30 40
40
a x > 3 b x ≤ −3 0 c x < 0 30 d x ≥ −20
20
10
–40 –30 –20 –10
–40 –30 –20 –10 0 10 20 30 40
132 13 Equations and inequalities