#### Answer

The solution is:
$$x = 12$$
To check if the solution is correct, we plug $12$ in for $x$ into the original equation to see if both sides of the equation are equal:
$$5(12) + 20 = 8(12) - 16$$
We simplify the equation by doing the multiplication first:
$$60 + 20 = 96 - 16$$
We then do the addition and subtraction:
$$80 = 80$$
Both sides are equal, so we know that the solution is correct.

#### Work Step by Step

To solve this equation, we need to isolate $x$ on one side of the equation and the constants on the other side.
We need to first subtract $5x$ on both sides to move all $x$ terms to one side of the equation:
$$20 = 3x - 16$$
We then add $16$ to both sides to move the constants to the other side of the equation:
$$3x = 36$$
To isolate $x$, divide by $3$ on both sides:
$$x = 12$$
To check if the solution is correct, we plug $12$ in for $x$ into the original equation to see if both sides of the equation are equal:
$$5(12) + 20 = 8(12) - 16$$
We simplify the equation by doing the multiplication first:
$$60 + 20 = 96 - 16$$
We then do the addition and subtraction:
$$80 = 80$$
Both sides are equal, so we know that the solution is correct.