persamaan linear

1. WAJA Mathematics PMR
LINEAR EQUATIONS
A. Solve Equations In The Form x + a = b.
EXAMPLE.
Solve the equation : x + 2 = 5
x + 2 = 5
x + 2 – 2 = 5 – 2
0 3
x + 0 = 3
What is left ?
x = 3,
So, x = 3 is the solution for x + 2 = 5.
ACTIVITY 1 :
(Fill in the boxes with the correct number)
x + 6 = 10
x + 6 = 10
x + 0 =
x =
So, x = is the solution for x + 6 = 10.
Page 1 of 11
This number must be
eliminated…How ?...
To solve this equation, any number on the left hand side except x must be eliminated. How
to eliminate the numbers on the left hand side ? Its easy actually…just add thesame number
to the left hand side but with opposite mark (+ / - ) and do the same to the right hand side…

2. WAJA Mathematics PMR
ACTIVITY 2 :
(Fill in the boxes with the correct number)
x + 50 = 100
x + 50 = 100
x + 0 =
x =
So, x = is the solution for x + 50 = 100.
ACTIVITY 3 :
(Fill in the boxes with the correct number)
x + 7 = – 3
x + 7 = – 3
x + 0 =
x =
So, x = is the solution for x + 7 = – 3.
Page 2 of 11
EXERCISE 1.
Solve the following equations.
1. x + 3 = 7 3. x + 10 = 15 5. x + 21 = 23
2. x + 9 = 12 4. x + 15 = 25 6. x + 21 = 30

3. WAJA Mathematics PMR
B. Solve Equations In The Form x – a = b.
EXAMPLE.
Solve the equation : x – 4 = 3
x – 4 = 3
x – 4 + 4 = 3 + 4
0 7
x – 0 = 7
What is left ?
x = 7
So, x = 7 is the solution for x – 4 = 3.
ACTIVITY 1 :
(Fill in the boxes with the correct number)
x – 8 = 3
x – 8 = 3
x – 0 =
x =
So, x = is the solution for x – 8 = 3.
Page 3 of 11
This number must be
eliminated…How ?..
To solve this equation, any number on the left hand side except x must be elimininated. How
to eliminate the numbers on the left hand side ? It is easy actually…just add an equal
number to the left hand side but with opposite mark (+ / - ) and do the same to the right hand

4. WAJA Mathematics PMR
ACTIVITY 2 :
(Fill in the boxes with the correct number)
x – 7 = 12
x – 7 = 12
x – 0 =
x =
So, x = is the solution for x – 7 = 12.
ACTIVITY 3 :
(Fill in the boxes with the correct number)
x – 12 = 15
x – 12 = 15
x – 0 =
x =
So, x = is the solution for x – 12 = 15.
C. Solve Equations In The Form ax = b.
Page 4 of 11
EXERCISES 2.
Solve the following equations.
1. x – 3 = 7 3. x – 10 = 15 5. x – 21 = 23
2. x – 9 = 12 4. x – 15 = 25 6. x – 20 = 40

5. WAJA Mathematics PMR
EXAMPLE.
Solve the equation : 3x = 12
3 x = 12
3
12
3
3
=
x
x = 4
What is left ?
x = 4
So, x = 4 is the solution for 3x = 12.
ACTIVITY 1 :
(Fill in the boxes with the correct number)
5 x = 10
5
10
5
5
=
x
x =
So, x = is the solution for 7 x = 21.
ACTIVITY 2 :
(Fill in the boxes with the correct number)
Page 5 of 11
This number must be
eliminated…How ?...
To solve this equation, any number on the left hand side except x must be eliminated.
How to eliminate the numbers on the left hand side ? It is easy actually…just divide
the number (coefficient of x) with the same number as the coefficient of x on the left
hand side… and do the same to the right hand side…
4
Express the fraction as a single
fraction in it simplest form.

6. WAJA Mathematics PMR
7 x = 21
7 x = 21
x =
So, x = is the solution for 7 x = 21.
ACTIVITY 3 :
(Fill in the boxes with the correct number)
10 x = 30
10 x = 30
x =
So, x = is the solution for 10 x = 30.
D. Solve Equations In The Form b
a
x
= .
EXAMPLE.
Page 6 of 11
EXERCISE 3.
Solve the following equations.
1. 3x = 15 3. 2x = 18 5. 10x = 20
2. 5x = 20 4. 7x = 28 6. 15x = 60

7. WAJA Mathematics PMR
Solve the equation : 3
6
=
x
3
6
=
x
636
6
×=×
x
x = 18
What is left ?
x =18
So, x = 18 is the solution for 3
6
=
x
.
ACTIVITY 1 :
(Fill in the boxes with the correct number)
7
3
=
b
373
3
×=×
b
b =
So, x = is the solution for 7
3
=
b
.
ACTIVITY 2 :
(Fill in the boxes with the correct number)
Page 7 of 11
This number must be
eliminated…How ?...
To solve this equation, any number on the left hand side except x must be
eliminated. How to eliminate the numbers on the left hand side ? It is easy
actually…just multiply the number with the same number as the numerator on the
left hand side… and do the same to the right hand side…

8. WAJA Mathematics PMR
5
6
=
b
6
b
x = 5 x
b =
So, x = is the solution for 5
6
=
b
.
ACTIVITY 3 :
(Fill in the boxes with the correct number)
3
10
=
b
10
b
x = 3 x
b =
So, x = is the solution for 3
10
=
b
.
E. Solve Equations In The Form ax + b = c.
EXAMPLE.
Page 8 of 11
EXERCISE 4.
Solve the following equations.
1. 5
4
=
x
3. 2
9
=
x
5. 5
10
=
x
2. 7
6
=
x
4. 3
12
=
x
6. 4
15
=
x

9. WAJA Mathematics PMR
Solve the following equation.
2 x + 4 = 10
Solution : (Elimination Method – step by step)
2 x + 4 – 4 = 10 – 4
2 x + 0 = 6
What is left ?
2 x = 6
2
6
2
2
=
x
What is left ?
x = 3
So, x = 3 is the solution for 2x + 4 = 10.
ACTIVITY 1 :
(Fill in the boxes with the correct number)
1. 3x + 5 = 14 2. 5x + 6 = 16
Page 9 of 11
To be eliminated
The integer that is added to the left hand side
(must be the same as the integer to be
eliminated but with the opposite mark)
The integer that is added to the right hand
side (must be the same as the integer that
is added to the left hand side)
a. eliminate the integer on the left hand side.
b. to eliminate the integer, add the same number on
the left hand side but with the opposite mark ( ―
or +)
d. and then eliminate the coefficient of x.
e. to eliminate the coeficient of x, divide it by an integer that
is equal to the coefficient of x.
f. the integer on the right hand side also divided by the same
integer.3
To be eliminated

10. WAJA Mathematics PMR
TRY THESE QUESTIONS TOO…
ACTIVITY 2 :
(Fill in the boxes with the correct number)
i. 3x – 5 = 10 ii. 5x – 6 = 4
Page 10 of 11
3x + 5 = 14
Fill in the box with a number that is the same
as the number on the left hand side.
3x + 5 = 14
3x =
And then eliminate coefficient 3
3x =
What is left ?
x =
Then, x = is the solution for 3x + 5 =
14.
5x + 6 = 16
BERUSAHA HINGGA
JAYA…
3x – 5 = 10
Fill in the box with a number that is the same
as the number on the left hand side.
3x – 5 = 10
3x =
And then eliminate coefficient 3
3x =
What is left ?
x =
Then, x = is the solution for 3x – 5 =
10.
5x – 6 = 4

11. WAJA Mathematics PMR
TRY THESE QUESTIONS TOO…
Page 11 of 11
EXERCISE 5.
Solve the following equations.
1. 2x + 7 = 1 5 4. 10x – 5= 15
2. 4x – 6 = 10 5. 12x – 7 =17
3. 3x + 12 = 15 6. 20x – 15 =25
BERUSAHA
HINGGA
JAYA…