The contrapositive of ` 2x +3 =9 Rightarrow x ne 4 ` is

Options

A. ` x =4 Rightarrow 2x + 3 ne 9`
B. ` x =4 Rightarrow 2x + 3=9`
C. ` x ne 4 Rightarrow 2x +3 ne 9`
D. ` x ne 4 Rightarrow 2x +3=9`

Answer

To find the contrapositive of the statement "2x + 3 = 9 ⇒ x ≠ 4", we follow these steps:

### Step 1: Identify the components of the implication
The given statement is in the form of "P ⇒ Q", where:
- P: 2x + 3 = 9
- Q: x ≠ 4

### Step 2: Write the negation of both components
To find the contrapositive, we need to negate both P and Q:
- Negation of P (¬P): 2x + 3 ≠ 9
- Negation of Q (¬Q): x = 4

### Step 3: Form the contrapositive
The contrapositive of "P ⇒ Q" is "¬Q ⇒ ¬P". Therefore, we can write:
- ¬Q ⇒ ¬P: x = 4 ⇒ 2x + 3 ≠ 9

### Step 4: Finalize the contrapositive statement
Thus, the contrapositive of the original statement is:
**x = 4 ⇒ 2x + 3 ≠ 9**

### Summary
The contrapositive of the statement "2x + 3 = 9 ⇒ x ≠ 4" is "x = 4 ⇒ 2x + 3 ≠ 9".

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