Solve the inequation ` sqrt(3x -8) lt -2 `

Options

A. `phi `
B. [1,2]
C. [12, `∞` ]
D. (1,12]

Answer

To solve the inequation \( \sqrt{3x - 8} < -2 \), we can follow these steps:

### Step 1: Analyze the Square Root
The expression \( \sqrt{3x - 8} \) represents the square root of \( 3x - 8 \). By definition, the square root of any real number is always non-negative (i.e., it is either positive or zero).

### Step 2: Set Up the Inequality
Given that \( \sqrt{3x - 8} < -2 \), we recognize that this is asking for the square root to be less than a negative number.

### Step 3: Conclusion from the Inequality
Since the square root cannot be negative, there are no values of \( x \) that can satisfy this inequality. Thus, we conclude that the inequality has no solution.

### Final Answer
The solution to the inequation \( \sqrt{3x - 8} < -2 \) is that there are no values of \( x \) that satisfy this condition.

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