Solving Linear Equations without Brackets


 
 
Concept Explanation
 

Solving Linear Equations without Brackets

Solving Linear Equations without Brackets:

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 equaton 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:

Example:  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

large Solve for m : 5m+frac{25}{4}=6

Right Option : D
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Explanation
Question : 2

If large frac {1}{x+1}+frac {1}{x+4}=0, then find the value of x:

Right Option : B
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Explanation
Question : 3

In    frac {a}{8}+frac {a}{4}=6,  the value of a is ___________________

Right Option : C
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Explanation
 
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