Answer
$x = \frac{23}{3}$
To check if our solution is correct, we plug it into the original equation:
$-2\sqrt {3(\frac{23}{3}) - 7} - 11 = -19$
Multiply to simplify:
$-2\sqrt {23 - 7} - 11 = -19$
Evaluate what is inside the radical:
$-2\sqrt {16} - 11 = -19$
Evaluate the radical:
$-2(4) - 11 = -19$
Multiply to simplify:
$-8 - 11 = -19$
Add to simplify:
$-19 = -19$
Work Step by Step
We need to isolate the radical, so we add $11$ to each side of the equation first:
$-2\sqrt {3x - 7} = -8$
Divide both sides by $-2$ to isolate the radical:
$\sqrt {3x - 7} = 4$
We need to get rid of the radical, so we square both sides of the equation:
$3x - 7 = 4^{2}$
Evaluate the right side of the equation:
$3x - 7 = 16$
Add $7$ to both sides of the equation to collect constants on the right side of the equation:
$3x = 23$
Divide both sides by $3$ to solve for $x$:
$x = \frac{23}{3}$
To check if our solution is correct, we plug it into the original equation:
$-2\sqrt {3(\frac{23}{3}) - 7} - 11 = -19$
Multiply to simplify:
$-2\sqrt {23 - 7} - 11 = -19$
Evaluate what is inside the radical:
$-2\sqrt {16} - 11 = -19$
Evaluate the radical:
$-2(4) - 11 = -19$
Multiply to simplify:
$-8 - 11 = -19$
Add to simplify:
$-19 = -19$
