Q. 298 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{6n+1}+4=8$

Step-by-Step Solution

Answer

The solution of the given equation is $n=2.5$.

Step 1. Given information.

The given equation is:

$\sqrt{6n+1}+4=8$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}\sqrt{6n+1}& =& 8-4\\ \sqrt{6n+1}& =& 4\end{array}$

Take square on both sides.

$\begin{array}{rcl}(\sqrt{6n+1}{)}^2& =& (4{)}^2\\ 6n+1& =& 16\\ 6n& =& 16-1\\ 6n& =& 15\end{array}$

Divide both sides by 6.

$\begin{array}{rcl}\frac{6n}{6}& =& \frac{15}{6}\\ n& =& 2.5\end{array}$

Step 3. Conclusion.

The solution of the given equation is $n=2.5$.