Sure, let's solve the equation step-by-step:
Given equation:
[tex]\[ \sqrt{2x} + 3 = 9 \][/tex]
### Step 1: Isolate the square root term
First, we want to isolate the square root term. To do this, we subtract 3 from both sides of the equation:
[tex]\[ \sqrt{2x} + 3 - 3 = 9 - 3 \][/tex]
[tex]\[ \sqrt{2x} = 6 \][/tex]
### Step 2: Remove the square root by squaring both sides
Next, we want to eliminate the square root. We do this by squaring both sides of the equation:
[tex]\[ (\sqrt{2x})^2 = 6^2 \][/tex]
[tex]\[ 2x = 36 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Finally, we solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{36}{2} \][/tex]
[tex]\[ x = 18 \][/tex]
So the solution to the equation [tex]\(\sqrt{2x} + 3 = 9\)[/tex] is [tex]\(x = 18\)[/tex].
Thus, the correct answer is [tex]\( 18 \)[/tex].
