Finding Solution of Linear Equation in One Variable


 
 
Concept Explanation
 

Finding Solution of Linear Equation in One Variable

Solving an equation means finding the value of the variable which satisfies it.

Rules for Solving Linear Equations In One Variable:

There are certain facts about equality.

Rule 1:   Same quantity (number) can be added to both sides of an equation without changing the equality.

Rule 2:   Same quantity can be subtracted from both sides of an equation without changing the equality.

Rule 3:   Both sides of an equation may be multiplied by the same non - zero number without changing the equality.

Rule 4:  Both sides of an equation may be divided by the same non - zero number without changing the equality.

These rules are used to solve the problems:

Illustration:  Solve the following equation and verify the result

: large frac{x}{5}+11=frac{1}{15} 

Solution:  We have, 

                          large frac{x}{5}+11=frac{1}{15}

           large Rightarrow ;;frac{x}{5}+11-11=frac{1}{15}-11         [ Subtracting 11 from both sides]

         large Rightarrow ;;frac{x}{5}=frac{1}{15}-11

       large Rightarrow ;;frac{x}{5}=frac{1-165}{15}

      large Rightarrow ;;frac{x}{5}=-frac{164}{15}

     large Rightarrow ;;5times frac{x}{5}=5times -frac{164}{15}

     large Rightarrow ;;x=-frac{164}{3}

large Rightarrow ;;x=-frac{164}{3};is ;the ;solution ;of ;the; given ;equation.

Verification Putting the vaue of x in LHS, we get

large =frac{x}{5}+11=frac{-164}{3}times frac{1}{5}+11=frac{-164}{15}+11=frac{-164+165}{15}=frac{1}{15}

large and, ; R.H.S; =frac{1}{15}

  large Therefore ; L.H.S = R.H.S. ; For;x=frac{-164}{3}

large Hence;x=frac{-164}{3}, large x=frac{-164}{3};is ;the ;solution ;of; the; given; equation.  

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If large frac {1}{x+1}+frac {1}{x+3}=0, then find the value of x:

Right Option : D
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Explanation
Question : 2

The solution of large frac{2x+11}{3x-11}=frac{5}{2} is:

Right Option : C
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Explanation
Question : 3

If large frac {x}{qp}+frac {x}{qr}+frac {x}{pr}=p+q+r, then find the value of x:

Right Option : A
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Explanation
 
 


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