Answer
$x = \frac{11}{3}$
To check if our solution is correct, substitute it back into the original equation:
$\sqrt {3(\frac{11}{3}) - 7} = 2$
Multiply factors within the radical:
$\sqrt {11 - 7} = 2$
Simplify the radical:
$\sqrt {4} = 2$
Evaluate the square root:
$2 = 2$
The two sides are equal; therefore, the solution is correct.
Work Step by Step
Square both sides of the equation:
$3x - 7 = 2^{2}$
Evaluate the right side of the equation:
$3x - 7 = 4$
Add $7$ to each side of the equation to solve for $x$:
$3x = 11$
Divide both sides of the equation by $3$:
$x = \frac{11}{3}$
To check if our solution is correct, substitute it back into the original equation:
$\sqrt {3(\frac{11}{3}) - 7} = 2$
Multiply factors within the radical:
$\sqrt {11 - 7} = 2$
Simplify the radical:
$\sqrt {4} = 2$
Evaluate the square root:
$2 = 2$
The two sides are equal; therefore, the solution is correct.