**Which x satisfies an equation :**

A solution to an equation is a value of a variable that makes the equation true.

**How to check which x satisfies an equation :**

- Apply the first value instead of x in the given equation.
- If the applied value satisfies the given equation,the we can decide that particular value is a solution.
- Otherwise we have to apply the next values.

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

Note :

Every linear equations will have only one value for the variable that we found in the given equation.

Every quadratic equations will have two values for the variable that we found in the given equation.

Like wise according to the degree of the polynomial, we will have number of solutions.

**Example 1 :**

What value of z is a solution to this equation?

z + 11 = 17

Options :

(a) z = 5 (b) z = 6

**Solution :**

Let us apply the first value of z that is 5 instead of z in the given equation.

5 + 11 = 17

16 ≠ 17

Since the above value do not satisfies the given equation, we can decide that z = 5 is not the solution.

Now apply the second value of z that is 6 instead of z in the given equation.

6 + 11 = 17

17 = 17

Since the above value satisfies the given equation, we can decide that z = 5 is the solution.

Hence 5 is the solution of the given equation.

**Example 2 :**

What value of p is a solution to this equation?

3P + 4 = 25

Options :

(a) P = 2 (b) P = 7

**Solution :**

Let us apply the first value of P that is 2 instead of P in the given equation.

3P + 4 = 25

3(2) + 4 = 25

6 + 4 = 25

10 ≠ 25

Since the above value do not satisfies the given equation, we can decide that P = 2 is not the solution.

Now apply the second value of P that is 7 instead of z in the given equation.

3P + 4 = 25

3(7) + 4 = 25

21 + 4 = 25

25 = 25

Since the above value satisfies the given equation, we can decide that p = 7 is the solution.

Hence 7 is the solution of the given equation.

**Example 3 :**

What value of x is a solution to this equation?

5x + 3 = 17 - 2x

Options :

(a) x = 2 (b) x = -1

**Solution :**

Let us apply the first value of x that is 2 instead of x in the given equation.

5(2) + 3 = 17 - 2(2)

10 + 3 = 17 - 4

13 = 13

Since the value satisfies the given equation, we donot have to check the second value. Because every linear equation will have only one solution.

Hence 2 in the solution of the given equation.

**Example 4 :**

What value of x is a solution to this equation?

12 - x = 8

Options :

(a) x = -4 (b) x = 4

**Solution :**

Let us apply the first value of x that is -4 instead of x in the given equation.

12 - (-4) = 8

12 + 4 = 8

16 ≠ 8

Now apply the second value of x that is 4 instead of x in the given equation.

12 - 4 = 8

8 = 8

Hence the solution of the given equation is 4.

**Example 5 :**

What value of q is a solution to this equation?

q/6 = 7

Options :

(a) q = 42 (b) q = 1

**Solution :**

Let us apply the first value of q that is 42 instead of q in the given equation.

42/6 = 7

7 = 7

Hence the solution of the given equation is 42.

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

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