WHICH VALUE OF X SATISFIES THE EQUATION

About "Which value of x satisfies the equation"

Which value of x satisfies the equation :

A solution to an equation is a value of a variable that makes the equation true. From the statement "Which value of x satisfies the equation", we need to understand that, we have to find the value of x from the given question.

Let us see some example problems based on the above concept.

Example 1 :

Which value of x is the solution of the equation

(2/3) x + (1/2) = (5/6) ?

Solution :

(2/3) x + (1/2)  =  (5/6)

(2x/3)  + (1/2)  =  (5/6)

(4x + 3)/6  =  (5/6)

Multiply 6 on both sides

4x + 3  =  5

Subtract 3 on both sides

4x + 3 - 3  =  5 - 3

4x =  2

Divide by 4 on both sides

4x/4  =  2/4

x  =  1/2

Hence the value 1/2 will satisfy the above equation.

Example 2 :

Which value of x is the solution of the equation

(2/3) x + (x/6) = 5 ?

Solution :

(2x/3) + (x/6) = 5

(4x/6) + (x/6) = 5

(4x + x)/6  =  5

5x/6  =  5

Multiply by 6 on both sides

5x  =  5 (6)

5x  =  30

Divide by 5 on both sides

x  =  30/5  =  6

Hence the value 6 will satisfy the above equation.

Example 3 :

The number of people on the school board is represented by x. Two subcommittees with an equal number of members are formed, one with (2x/3) − 5 members and the other with x/4 members. How many people are on the school board?

Solution :

From the above question, we come to know that we have to solve for x, that makes the statement true.

(2x/3) − 5  =  x/4

(2x - 15)/3  =  x/4

Multiply 3 on both sides

2x - 15  =  3x/4

Multiply by 4 on both sides

4(2x - 15)  =  3x

8x - 60   =  3x

Subtract 3x on both sides

8x - 3x  -  60  =  0

5x - 60  =  0

Add by 60 on both sides

5x - 60 + 60  =  0  + 60

5x  =  60

Divide by 5 on both sides

x  = 60/5

x  =  12

Example 4 :

What is the value of x in the equation

(x − 2)/3 + 1/6 = 5/6 ?

Solution :

(x − 2)/3 + 1/6 = 5/6

(2(x - 2) + 1)/6  =  5/6

multiply by 6 on both sides

(2x - 4 + 1)  =  5

2x - 3  =  5

2x - 3 + 3  =  5 + 3

2x  =  8

Divide by 2 on both sides

x  = 8/2

x  =  4

After having gone through the stuff given above, we hope that the students would have understood "Which value of x satisfies the equation".

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