#### Answer

$$x = 8$$

#### Work Step by Step

To solve this equation, we first want to get rid of the fractions. We do this by multiplying each term by the least common denominator, which, in this case, is $4$:
$$4(\frac{x}{2}) + 4(7) = 4(13) - 4(\frac{x}{4})$$
We divide out common factors to get rid of the fractions:
$$2x + 28 = 52 - x$$
Add $x$ to both sides to isolate the variable on one side of the equation:
$$3x + 28 = 52$$
Subtract $28$ on both sides to move the constants to one side of the equation:
$$3x = 24$$
Divide by $3$ on both sides of the equation to solve for $x$:
$$x = 8$$