Certainly! Let's solve the given equation step-by-step:
Given equation:
[tex]\[ 3 \sqrt{d-5} = 9 \][/tex]
1. Isolate the square root term:
Divide both sides of the equation by 3 to isolate the square root term.
[tex]\[ \sqrt{d - 5} = \frac{9}{3} \][/tex]
Simplify the right side:
[tex]\[ \sqrt{d - 5} = 3 \][/tex]
2. Eliminate the square root:
Square both sides of the equation to eliminate the square root.
[tex]\[ (\sqrt{d - 5})^2 = 3^2 \][/tex]
Simplify both sides:
[tex]\[ d - 5 = 9 \][/tex]
3. Solve for [tex]\( d \)[/tex]:
Add 5 to both sides of the equation to solve for [tex]\( d \)[/tex].
[tex]\[ d = 9 + 5 \][/tex]
Simplify the right side:
[tex]\[ \d = 14 \][/tex]
So, the solution to the equation [tex]\( 3 \sqrt{d-5} = 9 \)[/tex] is:
[tex]\[ d = 14 \][/tex]
Thus, the correct answer is 14.
