The equation you're asking about is:

$\sqrt{3x + 45} + 1 = 7$

Steps to solve:

1. Isolate the square root term:
   Subtract 1 from both sides:

   $\sqrt{3x + 45} = 7 - 1$ $\sqrt{3x + 45} = 6$

2. Square both sides:
   This eliminates the square root on the left side:

   $(\sqrt{3x + 45})^2 = 6^2$ $3x + 45 = 36$

3. Solve for $x$:
   Subtract 45 from both sides:

   $3x = 36 - 45$ $3x = -9$

   Now, divide both sides by 3:

   $x = \frac{-9}{3}$ $x = -3$

Final Answer:

$x = -3$

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Would you like a more detailed explanation or help with another problem?

Here are 5 related questions:

1. How do you solve an equation involving a square root term?
2. What is the principle of squaring both sides in an equation?
3. How do you check if the solution $x = -3$ satisfies the original equation?
4. What are other methods for solving equations with square roots?
5. How do you handle equations that contain both a linear term and a square root term?

Tip: Always check your solution by substituting it back into the original equation to confirm it's correct!