Question

Solve each equation.

$\sqrt{2x+1}=3$

Short answer

The solution is$x=4$.

Step-by-step solution

Step 1. Given Information.

Given, to solve the equation $\sqrt{2x+1}=3$.

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l}\sqrt{2x+1}=3\\ {\left(\sqrt{2x+1}\right)}^2={\left(3\right)}^2\\ 2x+1=9\\ 2x=9-1\\ 2x=8\\ x=\frac{8}{2}\\ x=4\end{array}$

Checking if the value of x satisfies the equation:

$\begin{array}{l}\sqrt{2x+1}=3\\ \sqrt{2\left(4\right)+1}=3\\ \sqrt{8+1}=3\\ \sqrt{9}=3\\ 3=3\end{array}$

Hence the value of x satisfies the equation.

Step 3. Conclusion.

Hence, the solution is x=4.