Unit 12 Section 3 : Linear Equations 1

In this section we revise the solution of simple equations.
Reminder

Whatever you do to one side of an equation you must do to the other side: it is like keeping a set of scales balanced.

It is conventional to give the solution to an equation with the unknown value on the left hand side, and its value on the right hand side, e.g. x = 4 not 4 = x.

Example Questions

Look at how the following equations are solved.
(a) 11 = x + 6          11=x + 6[subtract 6 from both sides to get x on its own]
11 – 6=x + 6 – 6[note how the 'subtract 6' cancels out the 'add 6']
5=x[switch sides so the x is on the left]
x=5
(b) y – 3 = 8y – 3=8[add 3 to both sides to get y on its own]
y – 3 + 3=8 + 3[note how the 'add 3' cancels out the 'subtract 3']
y=11
(c) 15 = 5c15=5c[divide by 5 on both sides to get c on its own]
15 ũ 5=5c ũ 5[note how the 'divide by 5' cancels out the 'multiply by 5']
3=c[switch sides so the c is on the left]
c=3
(d)  w = 10
2
 w
2
=10[multiply by 2 on both sides to get w on its own]
 w Ũ 2
2
=10 Ũ 2[note how the 'multiply by 2' cancels out the 'divide by 2']
 w=20

Practice Questions

Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

Practice Question 1
Solve these equations:
(a) p + 10 = 17          
(b) q – 13 = 2
(c) 4r = 14
(d)  s = 4
3

Practice Question 2
The length of the rectangle shown below is 4 metres and the width is x metres.
The area of the rectangle is 8 mē.
(a) Write down an equation involving x.
(b) Solve your equation to find x.
(c) Work out the perimeter of the rectangle.

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Solve the following equations:
(a)x + 5 = 9
x =

(b)x + 11 = 12
x =

(c)7 + x = 9
x =

(d)x + 2 = 17
x =

(e)14 = x + 6
x =

(f)x – 2 = 10
x =

(g)x – 6 = 5
x =

(h)2 = x – 9
x =

(i)x + 3 = 0
x =

(j)x – 7 = 7
x =

(k)x + 12 = 7
x =

(l)x – 6 = –10
x =

Question 2
Solve the following equations:
(a)2x = 12
x =

(b)3x = 18
x =

(c)5x = 20
x =

(d)7x = 21
x =

(e)36 = 9x
x =

(f)5x = 0
x =

(g)80 = 10x
 
x =

(h)
 x = 5
2
x =

(i)
 x = 6
3
x =

(j)
9 =  x
4
x =

(k)
 x = 22
2
x =

(l)
 x = 4
7
x =

(m)4x = 2
 
x =

(n)
 x = 6
2
x =

(o)
 x = 0
10
x =

Question 3
Solve the following equations:
(a)x + 7 = 9
x =

(b)x – 6 = 8
x =

(c)3x = 33
x =

(d)
 x = 2
5
x =

(e)x + 2 = 13
 
x =

(f)5x = 35
 
x =

(g)4 + x = 15
x =

(h)7 = y – 9
y =

(i)42 = 6p
p =

(j)
90 =  q
9
q =

(k)5r = –10
 
r =

(l)
–4 =  s
8
s =

Question 4
The area of the rectangle shown below is 18 cmē.
(a) Write down an equation involving x. Make sure the part with x in is on the left.

(b) Solve your equation.
x =

(c) Write down the perimeter of the rectangle.
cm

Question 5
The perimeter of the triangle shown below is 17 cm.
(a) Write down an equation and solve it to find x.
x =

(b) Write down the difference between the longest and shortest sides in the triangle.
cm

You have now completed Unit 12 Section 3
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Produced by A.J.Reynolds October 2007