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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