Question

2 + \sqrt{x + 1} = 4

Explanation:

Step1: Isolate the square root term

Subtract 2 from both sides of the equation \(2 + \sqrt{x + 1}=4\).
\(2 + \sqrt{x + 1}-2 = 4 - 2\)
Simplifying, we get \(\sqrt{x + 1}=2\).

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{x + 1}=2\) to get rid of the square root.
\((\sqrt{x + 1})^2=2^2\)
Which simplifies to \(x + 1 = 4\).

Step3: Solve for x

Subtract 1 from both sides of the equation \(x + 1 = 4\).
\(x + 1-1 = 4 - 1\)
Simplifying, we find \(x = 3\).

Step4: Check the solution (optional but good practice)

Substitute \(x = 3\) back into the original equation:
Left - hand side: \(2+\sqrt{3 + 1}=2+\sqrt{4}=2 + 2=4\)
Right - hand side: \(4\)
Since the left - hand side equals the right - hand side, \(x = 3\) is a valid solution.

Answer:

\(x = 3\)