1. Whiteboardmaths.com
© 2008 All rights reserved 5 7 2 1

2.   Refresher 5(2x - 3) Solving Equations 2x + 5 = x + 10 x + 5 = 10
Remember:
1. We have previously solved simple equations like the one shown and we looked at the analogy of scales in which both sides are balanced.
2x + 5 = x + 10
x + 5 = 10
x = 5
2x + 5
x + 10
2. We have previously expanded single brackets as shown below.
5(2x - 3)
means 5 x (2x - 3) = 10x - 15
+ x + = +
+ x - = -
- x + = -
- x - = +
3. We are familiar with the rules for signs when multiplying.
Unlike signs give a negative 
Refresher
We now need to know that the same rules apply for division. 

3. Ex Q’s 1 Solving Equations 7x + 5 = 2x - 10 6x - 2 = 1 + 2x
Example Questions
7x + 5 = 2x - 10
Example Question 1: solve
6x - 2 = 1 + 2x
Example Question 2: solve
Subtract 2x from both sides
Subtract 2x from both sides
5x + 5 = - 10
Subtract 5 from both sides
4x - 2 = 1
Add 2 to both sides
5x = - 15
4x = 3
Divide both sides by 5
Divide both sides by 4
x = -3
x = ¾
8 - 3x = 10 - x
Example Question 3: solve
2x + 9 = 1 - 3x
Example Question 4: solve
Add x to both sides
Add 3x to both sides
8 - 2x = 10
Subtract 8 from both sides
5x + 9 = 1
Subtract 9 from both sides
Ex Q’s 1
- 2x = 2
5x = -8
Divide both sides by 5
Divide both sides by -2
x = -1
x = -1.6

4. Questions 1 Solving Equations (a) 6x + 8 = 2x - 12 x = - 5
Solve the following equations
(a) 6x + 8 = 2x - 12
x = - 5
(b) 5x - 4 = x
x = 3
(c) 9 + 3x = x
x = ¾
(d) 3 - 7x = 7 + x
x = -½
(e) 2x - 7 = x
x = 2
(f) 9x + 25 = 5 + x
x = - 2½
(g) 7x + 8 = x
x = - 1/3
Questions 1

5. Ex Q’s 2 Brackets Solving Equations 2(x + 1) = x + 5
Example Questions With Brackets
2(x + 1) = x + 5
Example Question 1: solve
3(x - 1) = 2(x + 7)
Example Question 2: solve
2x + 2 = x + 5
3x - 3 = 2x + 14
x + 2 = 5
x - 3 = 14
x = 3
x = 17
3(x - 2) - 2(x + 1) = 5
Example Question 3: solve
7(x - 2) - 4 = 2(x + 2)
Example Question 4: solve
3x x - 2 = 5
7x = 2x + 4
x - 8 = 5
7x = 2x + 4
Ex Q’s 2 Brackets
x = 13
5x = 4
5x = 22
x = 4.4

6. Questions 2 Solving Equations (a) 8(x + 1) = 2(x + 16) x = 4
Solve the following equations
(a) 8(x + 1) = 2(x + 16)
x = 4
(b) 10(x + 1) = 7(x + 4)
x = 6
(c) 6(x - 5) = 5(x - 4)
x = 10
(d) 3(x + 2) = 2(x - 1)
x = -8
(e) 7(x - 2) - 3 = 2(x + 2)
x = 4.2
(f) 3(x + 1) + 2(x + 2) = 10
x = 0.6
(g) 5(x - 3) + 3(x + 2) = 7x
x = 9
x = -2 1 3
(h) 2x - 3(x + 2) = 2x + 1
Questions 2

7. Ex Q’s 3 Fractions Solving Equations x + 2 5 = x + 4 7 = 35(x + 2) 5
Example Questions Involving Fractions
Example Question 1: solve
x + 2 5 =
x + 4 7
Multiply both sides by 35, the common denominator of 5 and 7. 7 5
Cancel common factors and expand brackets. =
35(x + 2) 5
35(x + 4) 7 a b = c d
 da = bc
Note that in general if 1 1
7x + 14 =
5x + 20 4 8 = 6 12
 12 x 4 = 8 x 6 10 5 3
 3 x 10 = 5 x 6
2x + 14 = 20 2x = 6
x = 3
Ex Q’s 3 Fractions
This method of cross-multiplying combined with mentally expanding the brackets allows us to omit some steps and is therefore more efficient.

8. Solving Equations x - 5 5 = x - 2 8 5x - 1 7 = 7x + 3 12 8x - 40 =
Example Questions Involving Fractions
Example Question 2: solve
x - 5 5 =
x - 2 8
Example Question 3: solve
5x - 1 7 =
7x + 3 12
8x - 40 =
5x - 10
60x - 12 =
49x + 21
3x - 40 =
- 10
11x - 12 = 21 3x = 30
11x = 33
x = 10
x = 3

9. Questions 3 Solving Equations x = 6 x = 6 x = 7 x = 4 x = 13 x = 4
Solve the following equations
x + 1 7 =
x + 6 12
2x + 3 5 =
4x + 9 11
x = 6
x = 6 a. e.
x + 2 9 =
x + 4 11
3x + 2 2 =
6x + 11 5
x = 7
x = 4 b. f.
x - 1 3 =
x + 4 8
9x - 5 7 =
6x + 2 5
x = 13
x = 4 c. g.
x - 4 8 =
x - 1 11
3x - 8 4 =
2x - 3 5
x = 12
x = 4 d. h.
Questions 3

10. Ex Q’s 4 Problems Solving Equations 5n + 7 = 52 2(2x + 4) = 56 5n = 45
Problems leading to Simple Equations
Example Question 1
When a certain number is multiplied by 5 and then has 7 added to the result the answer is 52. Find the number.
Example Question 2
A rectangle has a perimeter of 56 cm. If Its length is 4cm longer than its width. Find the area of the rectangle.
Let n be the number then:
Let x cm be the width of the rectangle then:
5n + 7 = 52
2(2x + 4) = 56
5n = 45
4x + 8 = 56
x + 4 x
n = 9
4x = 48
x = 12
Ex Q’s 4 Problems
 area = 12 x 16 = 192 cm2

11. Solving Equations n + n + 1 + n + 2 = 81 3n + 3 = 81
Problems leading to Simple Equations
Example Question 3
Find three consecutive numbers whose sum is 81.
Example Question 4
Two angles of a triangle are 30 degrees and 75 degrees larger than the smallest angle. Find all three angles of the triangle.
Let n be the smallest number then:
n + n n + 2 = 81
Let xo be the smaller angle then:
3n + 3 = 81
x + x x + 75 = 180
3n = 78
3x = 180
n = 26
3x = 75
The numbers are 26, 27 and 28
x = 25
The angles are o, 55o, and 100o

12. Questions 4 Solving Equations 26, 28 and 30 12 5400 m2
Problems leading to Simple Equations
Question 1
Question 3
When a certain number is multiplied by 9 and then has 4 subtracted from the result, the answer is104. Find the number.
The sum of three consecutive even numbers is 84. Find them
26, 28 and 30 12
Question 2
Question 4
A rectangular playground is 30 m longer than its width. If its perimeter is 300m find its area.
Three angles of a quadrilateral are 55 degrees, 65 degrees and 120 degrees larger than the smallest angle. Find all four angles of the quadrilateral.
5400 m2
The angles are o, 85o, 95o and 150o
Questions 4

13. Worksheets Questions 1 Questions 2 (a) 6x + 8 = 2x - 12
(b) 5x - 4 = x
(c) 9 + 3x = x
(d) 3 - 7x = 7 + x
(e) 2x - 7 = x
(f) 9x + 25 = 5 + x
(g) 7x + 8 = x
(a) 8(x + 1) = 2(x + 16)
(c) 6(x - 5) = 5(x - 4)
(d) 3(x + 2) = 2(x - 1)
(b) 10(x + 1) = 7(x + 4)
(e) 7(x - 2) - 3 = 2(x + 2)
(f) 3(x + 1) + 2(x + 2) = 10
(g) 5(x - 3) + 3(x + 2) = 7x
(h) 2x - 3(x + 2) = 2x + 1
Questions 1
Questions 2
Worksheets

14. Solving Equations x + 1 x + 6 2x + 3 4x + 9 = 7 12 5 x + 2 x + 4
Worksheet 2
Solving Equations
Solve the following equations
x + 1 7 =
x + 6 12 a.
x + 2 9
x + 4 11 b.
x - 1 3 8 c.
x - 4 d.
2x + 3 5
4x + 9 e.
3x + 2 2
6x + 11 f.
9x - 5
6x + 2 g.
3x - 8 4
2x - 3 h.

15. Solving Equations Problems leading to Simple Equations Question 3
Worksheet 3
Solving Equations
Problems leading to Simple Equations
Question 1
Question 3
When a certain number is multiplied by 9 and then has 4 subtracted from the result, the answer is104. Find the number.
The sum of three consecutive even numbers is 84. Find them
Question 2
Question 4
A rectangular playground is 30 m longer than its width. If its perimeter is 300m find its area.
Three angles of a quadrilateral are 55 degrees, 65 degrees and 120 degrees larger than the smallest angle. Find all four angles of the quadrilateral.