# DETERMINE IF GIVEN VALUE IS A SOLUTION OF THE EQUATION

Determine If Given Value of the Variable is a solution of the equation

Here we are going to see how to determine if the given value of the variable is a solution of the equation.

The solution of an equation is the set of all values that, when substituted for unknowns, make the equation true.

## Determine If Given Value of the Variable is a Solution of the Equation - Practice questions

Question 1 :

Give any two examples for linear equations in one variable.

Solution :

x + 5  =  0, y - 3  =  0

Question 2 :

Check whether 1/4 is a solution of the equation 3(x + 1) = 3(5–x) – 2(5 + x).

Solution :

In order to check if the 1/4 is the solution of the given equation, we have apply the value of x in the equation.

3(x + 1) = 3(5 – x) – 2(5 + x).

3((1/4) + 1) = 3(5 – (1/4)) – 2(5 + (1/4))

3(5/4)  =  3(19/4) - 2(21/4)

(15/4)  =  (57/4) - (42/4)

(15/4)  =  (57 - 42)/4

15/4  =  15/4

Since 1/4 makes the given equation true, it is the solution.

## Solving Linear Equations in Fractions

Question 1 :

Solve the following linear equations

(i)  2(x + 1) / 3  =  3(x - 2) / 5

Solution :

2(x + 1) / 3  =  3(x - 2) / 5

Since we have fractions on either sides, we have to do cross multiplication.

10(x + 1)  =  9(x - 2)

10x + 10  =  9x - 18

10x - 9x  =  -18 + 10

x  =  -8

Hence the solution is -8.

(ii)  2/(x + 1)  =  4 - (x/(x + 1))

Solution :

2/(x + 1)  =  4 - (x/(x + 1))

2/(x + 1)  =  [4(x + 1) - x]/(x + 1)

2  =  [4(x + 1) - x]

2  =  4x + 4 - x

2  =  3x + 4

3x  =   2 - 4

3x  =  -2

x  =  -2/3

Hence the solution is -2/3.

After having gone through the stuff given above, we hope that the students would have understood, "determine if given value of the variable is a solution of the equation".

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