Solve:

[tex]\[ \sqrt{x+3} + 9 = 7 \][/tex]

A. [tex]\( x = 1 \)[/tex]

B. [tex]\( x = 5 \)[/tex]

C. [tex]\( x = -5 \)[/tex]

D. No solution



Answer :

To solve the equation
[tex]\[ \sqrt{x + 3} + 9 = 7 \][/tex]
we will isolate the square root term and analyze the situation step-by-step.

1. Isolate the Square Root Term:
Start by subtracting 9 from both sides of the equation:
[tex]\[ \sqrt{x + 3} = 7 - 9 \][/tex]

2. Simplify the Right Side:
Simplify the right side of the equation:
[tex]\[ \sqrt{x + 3} = -2 \][/tex]

3. Analyze the Result:
Recall that the square root of a number represents a non-negative value, that is:
[tex]\[ \sqrt{x + 3} \geq 0 \][/tex]
Therefore, it is impossible for the square root of any number to be negative. Thus, the equation
[tex]\[ \sqrt{x + 3} = -2 \][/tex]
cannot have any real solutions.

Hence, the given equation
[tex]\[ \sqrt{x + 3} + 9 = 7 \][/tex]
has no solution.

Given this logical analysis, we conclude that the equation has:
[tex]\[ \text{No solution} \][/tex]