Let's start by interpreting the equation provided. It seems like there might be a minor misunderstanding in the equation format. Based on what you've written, it looks like you're trying to solve for \( x \) in the following equation:
\[ 2 \sqrt{3x + 4} - 9 = 13 \]
To solve for \( x \), we will first isolate the square root term. Here are the steps:
- Add 9 to both sides:
\[ 2 \sqrt{3x + 4} = 22 \]
- Divide both sides by 2:
\[ \sqrt{3x + 4} = 11 \]
- Square both sides to eliminate the square root:
\[ 3x + 4 = 121 \]
- Subtract 4 from both sides:
\[ 3x = 117 \]
- Divide by 3:
\[ x = 39 \]
So, the solution to the equation is:
\[ \boxed{39} \]
Always remember to check if the obtained solution satisfies the original equation:
Plugging \( x = 39 \) back into the original equation:
\[ 2 \sqrt{3(39) + 4} - 9 = 13 \]
Calculating inside the square root:
\[ 3(39) + 4 = 117 + 4 = 121 \]
So we have:
\[ 2 \sqrt{121} - 9 = 13 \]
Since \( \sqrt{121} = 11 \):
\[ 2(11) - 9 = 13 \implies 22 - 9 = 13 \implies 13 = 13 \]
The solution checks out, confirming that \( x = 39 \) is indeed correct.