**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

Add 3 on both sides

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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