Question

Solve each equation.

$3+\sqrt{x+1}=5$

Short answer

The solution is$x=3$.

Step-by-step solution

Step 1. Given Information.

Given, to solve the equation $3+\sqrt{x+1}=5$.

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l}3+\sqrt{x+1}=5\\ \sqrt{x+1}=5-3\\ \sqrt{x+1}=2\\ {\left(\sqrt{x+1}\right)}^2={\left(2\right)}^2\\ x+1=4\\ x=4-1\\ x=3\end{array}$

Checking if the value of x satisfies the equation:

$\begin{array}{l}3+\sqrt{x+1}=5\\ 3+\sqrt{3+1}=5\\ 3+\sqrt{4}=5\\ 3+2=5\\ 5=5\end{array}$

Hence the value of x satisfies the equation.

Step 3. Conclusion.

Hence, the solution is x=3.