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SAI International School
CLASS - VIII

Mathematics
CHAPTER-2: Linear Equation in one variableLesson Notes-5

SUBTOPICS :REDUCING EQUATIONS TO SIMPLER FORM

The standard form of linear equations in one variable is represented as:
ax + b = 0

Where,
 ‘a’ and ‘b’ are real numbers, and
 both ‘a’ and ‘b’ are not equal to zero.
Thus, is the formula of linear equation in one variable is ax + b = 0.

6 +1 −3
Example 1: Solve + 1 =
3 6
6 +1 −3
Solution: We have + 1 =
3 6

6(6 +1) 6 ( −3)
or + 6 × 1 = (Multiplying both sides by 6**)
3 6
or 2 (6x + 1) + 6 = x – 3

or 12x + 2 + 6 = x – 3 (opening the brackets)

or 12x + 8 = x – 3

or 12x – x + 8 = – 3

or 11x + 8 = – 3

or 11x = –3 – 8

or 11x = –11

or x = – 1 (required solution)

**Why 6? Because it is the smallest multiple (or LCM) of the given denominators.

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