# How do you solve 7 + sqrt[2x - 1] = 10?

Aug 5, 2015

$x = 5$

#### Explanation:

First, start by isolating the readical on one side of the equation. This can be done by adding $- 7$ to both sides

$\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} + \sqrt{2 x - 1} = 10 - 7$

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

To get rid of the radical term, square both sides of the equation

${\left(\sqrt{2 x - 1}\right)}^{2} = {3}^{2}$

$2 x - 1 = 9$

$2 x = 10 \implies x = \frac{10}{2} = \textcolor{g r e e n}{5}$