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Solving Linear Equations in One Variable

To solve a linear equations with one variable, first simplify the equation by bringing all variable
terms to one side and all constant terms to the other side. If fractions are present in the equation,
then multiply both sides of the equation by the LCM of denominators to eliminate the fractions.

Rules for Solving a Linear Equation

1. To solve a linear equation using systematic method, the same non-zero number can be:
l added to both sides of the equation.

l subtracted from both sides of the equation.

l multiplied to both sides of the equation.
l used to divide both sides of the equation.

2. Transpose any term from either sides with the change in its sign. On transposing, the signs
are changed from: + to –, – to +, × to ÷, and ÷ to ×.

3. Cross-multiply the denominator of the term of one side with the numerator of the term on
the other side.

We have learnt the systematic (Balancing) and transposing Remember
methods earlier. Let us recall them through few examples.
The two sides (LHS and RHS) of an
Example 2: Find the solution of the equation 3x + 2 = 10. equation must be equal or balanced.
Solution: We have, 3x + 2 = 10

Using the balancing method, subtract 2 from both sides of the equation.

⇒ 3 x + 2 – 2 = 10 – 2 ⇒ 3x = 8
Now, divide both sides by 3.

3x 8 8
⇒ = ⇒ x =
3 3 3
8
Thus, x = is the solution of the given equation.
3
Example 3: Find the solution of the equation 7 – p = 11.
4
7
Solution: We have, – p = 11
4
7
⇒ –p = 11 – (Transposing 7 to RHS)
4 4

44 7 37
−
⇒ –p = ⇒ –p =
4 4
37
⇒ p = – (Multiplying both sides by –1)
4
37
Thus, p = – is the solution of the given equation.
4

37 Linear Equations in One Variable