Answer
$x = \frac{11}{2}$
To check if our solution is correct, we plug it into the original equation:
$3\sqrt {2(\frac{11}{2}) + 5} + 12 = 24$
Multiply to simplify:
$3\sqrt {11 + 5} + 12 = 24$
Evaluate what is inside the radical:
$3\sqrt {16} + 12 = 24$
Evaluate the radical:
$3(4) + 12 = 24$
Multiply to simplify:
$12 + 12 = 24$
Add to simplify:
$12 = 12$
Work Step by Step
We need to isolate the radical, so we subtract $12$ from each side of the equation first:
$3\sqrt {2x + 5} = 12$
Divide both sides by $3$ to isolate the radical:
$\sqrt {2x + 5} = 4$
We need to get rid of the radical, so we square both sides of the equation:
$2x + 5 = 4^{2}$
Evaluate the right side of the equation:
$2x + 5 = 16$
Add $9$ to both sides of the equation to collect constants on the right side of the equation:
$2x = 11$
Divide both sides by $2$ to solve for $x$:
$x = \frac{11}{2}$
To check if our solution is correct, we plug it into the original equation:
$3\sqrt {2(\frac{11}{2}) + 5} + 12 = 24$
Multiply to simplify:
$3\sqrt {11 + 5} + 12 = 24$
Evaluate what is inside the radical:
$3\sqrt {16} + 12 = 24$
Evaluate the radical:
$3(4) + 12 = 24$
Multiply to simplify:
$12 + 12 = 24$
Add to simplify:
$12 = 12$
