Q. 322 - Intermediate Algebra

Question

In the following exercises, solve.

$3\sqrt{7y+1}-10=8$

Step-by-Step Solution

Answer

The solution of the given equation is $y=5$.

Step 1. Given information.

The given equation is:

$3\sqrt{7y+1}-10=8$

Step 2. Simplify the equation.

The given equation can be written as:

$\begin{array}{rcl}3\sqrt{7y+1}& =& 8+10\\ 3\sqrt{7y+1}& =& 18\end{array}$

Divide both sides by 3.

$\begin{array}{rcl}\sqrt{7y+1}& =& \frac{18}{3}\\ \sqrt{7y+1}& =& 6\end{array}$

Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{7y+1}{)}^2& =& (6{)}^2\\ 7y+1& =& 36\\ 7y& =& 36-1\\ 7y& =& 35\end{array}$

Divide both sides by 7.

$\begin{array}{rcl}\frac{7y}{7}& =& \frac{35}{7}\\ y& =& 5\end{array}$

Step 4. Conclusion.

The solution of the given equation is $y=5$.