Q. 319 - Intermediate Algebra

Question

In the following exercises, solve.
$3\sqrt{2x-3}-20=7$

Step-by-Step Solution

Answer

The solution of the given equation is $x=42$.

Step 1. Given information.

The given equation is:

$3\sqrt{2x-3}-20=7$

Step 2. Simplify the equation.

The given equation can be written as:

$\begin{array}{rcl}3\sqrt{2x-3}& =& 7+20\\ 3\sqrt{2x-3}& =& 27\end{array}$

Divide both sides by 3.

$\begin{array}{rcl}\sqrt{2x-3}& =& \frac{27}{3}\\ \sqrt{2x-3}& =& 9\end{array}$

Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{2x-3}{)}^2& =& (9{)}^2\\ 2x-3& =& 81\\ 2x& =& 81+3\\ 2x& =& 84\end{array}$

Divide both sides by 2.

$\begin{array}{rcl}\frac{2x}{2}& =& \frac{84}{2}\\ x& =& 42\end{array}$

Step 4. Conclusion.

The solution of the given equation is $x=42$.