#### Answer

$x=\{-3,\frac{5}{3}\}$

#### Work Step by Step

"Three times a number is increased by 2" is written as $3x+2$.
The equation can be written as:
$(3x+2)^2=49$
Take the square root of each side.
$\sqrt{(3x+2)^2}=\sqrt{49}$
Simplify.
$3x+2=\pm7$
Subtract 2 from each side.
$3x+2-2=\pm7-2$
Simplify
$3x=7-2$ or $3x=-7-2$
$3x=5$ or $3x=-9$
Divide each side by 3.
$3x\div3=5\div3$ or $3x\div3=-9\div3$
$x=\frac{5}{3}$ or $x=-3$
State as a solution set.
$x=\{-3,\frac{5}{3}\}$