Class 8 Maths Linear Equations in One Variable | Reducing equations to simpler form |

__Reducing equations to simpler form__

Equations can be reduced to simpler form by

- Removing the denominators of both the sides.
- Opening the brackets.

Example, an equation is (6x + 1)/3 + 1 = (x - 3)/6

**Removing the denominators** by multiplying both sides by 6 because it is the LCM of the denominators of both sides,

6*(6x + 1)/3) + 1*6 = ((x - 3)/6)*6

- 2(6x + 1) + 6 = x - 3

**Opening the brackets**,

- 12x + 2 + 6 = x - 3
- 12x + 8 = x - 3

Adding 3 both sides,

- 12x + 8 + 3 = x - 3 + 3
- 12x + 11 = x

Transposing 11 to RHS and x to LHS,

- 12x - x = -11
- 11x = -11

Dividing both sides by 11,

- x = -1
- Cross-Multiplication

Example, an equation is (x + 1)/(2x + 3) = 3/8

**By cross-multiplication,**the denominator of LHS gets multiplied with numerator of RHS and vice-versa,

So, 8 * (x + 1) = 3 * (2x + 3)

- 8x + 8 = 6x + 9 (opening the brackets)
- 8x - 6x = 9 - 8 (transposing 6x and 8 other sides)
- 2x = 1
- x = 1/2 (Dividing both sides by 2)

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