Linear equation in one variable

2. Linear equation in one variable:
An equation of one variable and first order is called a
linear equation in one variable such an equation has
only one solution. A solution is also called the ‘root’ of
the given equation. An equation that can be written in
the form,
ax + b = 0,
Where a and b are real numbers and a ≠ o.
Following are some examples:
a) 2x + 3 = 0
x 1 2
b)
3 2 3
+ =
c) 5(3x+2) - 2 = - 2(1-7x)

3. Example-1
Solve the equation x – 4 = 5.
Solution:
Since x – 4 = 5
x = 5 + 4
x = 9
Example-2
Solve the equation 3x – 4 = 5.
Solution:
Since 3x – 4 = 5
3x = 5 + 4
3x = 9
9
x
3
=
x = 3

4. Example-3
Solve the equation 3-{2(1-x)-x} = 4
Solution:
Since 3-{2(1-x)-x} = 4
3-{2-2x-x} = 4
3-(2-3x) = 4
3-2+3x = 4
1+3x = 4
3x = 4-1
3x = 3
3
x
3
=
x = 1

5. Example-4
Solve the equation
x 5 x 3 5
7 4 14
+ −
+ =
Solution:
x 5 x 3 5
since
7 4 14
4(x 5) 7(x 3) 5
28 14
4x 20 7x 21
5
2
+ −
+ =
+ + −
=
+ + −
=
11x 1
5
2
11x 1 5x 2
11x 1 10
11x 10 1
11x 11
11
x
11
x 1
−
=
− =
− =
= +
=
=
=

6. Example-5
Solve the equation
x (x 3)
1
4 6
−
− =
Solution:
x (x 3)
1
4 6
multiplying throghout by the LCM (2 x 2 x 3) of the denominators (which is 12)
x 3x
12 12 12(1)
64
3x 2(x 3) 12
3x 2x 6 12
x 6 12
x 12 6
x 6
−
− =
−  − =   
   
− − =
− + =
+ =
= −
=