To solve the equation [tex]\(\sqrt{x+5} - 3 = 4\)[/tex], we need to follow these steps carefully:
1. Isolate the square root term:
First, add 3 to both sides to isolate the term with the square root.
[tex]\[
\sqrt{x+5} - 3 + 3 = 4 + 3
\][/tex]
Simplifying this, we get:
[tex]\[
\sqrt{x+5} = 7
\][/tex]
2. Eliminate the square root:
Next, square both sides of the equation to remove the square root.
[tex]\[
(\sqrt{x+5})^2 = 7^2
\][/tex]
This simplifies to:
[tex]\[
x + 5 = 49
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, solve for [tex]\( x \)[/tex] by subtracting 5 from both sides.
[tex]\[
x + 5 - 5 = 49 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
x = 44
\][/tex]
Thus, the solution to the equation [tex]\(\sqrt{x+5} - 3 = 4\)[/tex] is:
[tex]\[
x = 44
\][/tex]
So the correct answer is:
[tex]\[
x = 44
\][/tex]
