Answer
$x = 5$
Work Step by Step
Isolate the radical:
$\sqrt {2x - 1} = 3$
Square both sides of the equation to eliminate the radical:
$2x - 1 = 9$
Add $1$ to each side of the equation to isolate the $x$ term:
$2x = 10$
Divide both sides of the equation by $2$:
$x = 5$
To check if we have an extraneous solution, we substitute the solution into the original equation to see if the two sides equal one another.
$\sqrt {2(5) - 1} = 3$
Simplify the radicand:
$\sqrt {9} - 3 = 0$
Take the square root:
$3 - 3 = 0$
Combine like terms:
$0 = 0$
Both sides are equal; therefore, this solution is valid.
