# Reducing Equations to Simpler Form

## Notes

### Reducing Equations to Simpler Form:

When linear equations are in fractions then we can reduce them to a simpler form by -

• Taking the LCM of the denominator

• Multiply the LCM on both sides, so that the number will reduce without the denominator and we can solve them by the above methods.

## Example

Solve: (6x + 1)/3 + 1 = (x - 3)/6

Multiplying both sides of the equation by 6,

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

Check:
LHS = (6(-1) + 1) / 3 +1 = (-6+1)/3 + 1 = (-5)/3 + 3/3 = (-5+3)/3 = (-2)/3.

RHS = ((-1)-3) /6 = (-4)/ 6 = (-2)/3.

LHS = RHS     .......(as required)

## Example

Solve: 5x - 2(2x - 7) = 2(3x - 1) + 7/2

Let us open the brackets,

"LHS" = 5x - 4x + 14 = x + 14.

"RHS" = 6x - 2 + 7/2 = 6x - 4/2 + 7/2 = 6x + 3/2.

The equation is x + 14 = 6x + 3/2

or  14 = 6x - x + 3/2

or  14 = 5x + 3/2

or  14 - 3/2 = 5x

or  (28 - 3)/2 = 5x

or  25/2 = 5x

or x = 25/2 xx 1/5 = (5 xx 5)/(2 xx 5) = 5/2.

Therefore, required solution is x = 5/2

Check:

"LHS" = 5 xx 5/2 - 2(5/2 xx 2 - 7) = 25/2 - 2(5 - 7) = 25/2 - 2(- 2) = 25/2 + 4 = (25 +8)/2 = 33/2.

"RHS" = 2(5/2 xx 3 - 1) + 7/2 = 2(15/2 - 2/2) + 7/2 = (2 xx 13)/2 + 7/2 = (26 + 7)/2 = 33/2.

LHS = RHS.    ....(As required)

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Problems on Linear Equations in One Variable [00:16:12]
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