https://file.aiquickdraw.com/mathbot/file/172625712985498ng7mnt.jpg

The equation you provided is:

\[
a \sqrt{x + 1} = b
\]

We need to solve for \(x\). Here's the step-by-step process:

1. **Divide both sides by \(a\)**:
   \[
   \sqrt{x + 1} = \frac{b}{a}
   \]

2. **Square both sides to eliminate the square root**:
   \[
   x + 1 = \left(\frac{b}{a}\right)^2
   \]

3. **Subtract 1 from both sides**:
   \[
   x = \left(\frac{b}{a}\right)^2 - 1
   \]

Thus, the solution is:
\[
x = \left(\frac{b}{a}\right)^2 - 1
\]

Let me know if you'd like more details or have any questions.

Here are 5 related questions to explore:

1. What are the conditions on \(a\) and \(b\) for the solution to be valid?
2. How would you solve if there were a constant added to \(b\) on the right-hand side?
3. What if the square root was on both sides of the equation?
4. How would this solution change if \(x + 1\) were cubed instead of square rooted?
5. How do we interpret the geometric meaning of square roots in equations?

**Tip**: Always be cautious when squaring both sides of an equation, as it can introduce extraneous solutions. Always verify your solution by substituting back into the original equation.

Make x the subject of the formula a√(x + 1) = b.

Learn how to solve the equation a√(x + 1) = b step by step. This algebra problem involves square roots and basic manipulation, suitable for students in Grades 8-10.

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