Q49. - Algebra 2

Question

Solve each equation.

 

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

Step-by-Step Solution

Answer

The solution is $x=3$.

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.