Answer
$H$
Work Step by Step
First, we need to move all constants to the right side of the equation. To do this, we add $19$ to each side of the equation:
$\frac{7}{2}x = -13 + 19 + 2x$
Next, we want to move all $x$ terms to the left side of the equation. To do this, we subtract $2x$ from both sides of the equation:
$\frac{7}{2}x - 2x = -13 + 19$
Let's change $2x$ to a fraction with $2$ as its denominator so we can add the two fractions:
$\frac{7}{2}x - \frac{4}{2}x = -13 + 19$
Combine like terms:
$\frac{3}{2}x = 6$
To solve for $x$, we divide both sides by $\frac{3}{2}$. This means that we multiply by the reciprocal of this fraction, which is $\frac{2}{3}$:
$x = 6(\frac{2}{3})$
Multiply to simplify:
$x = \frac{12}{3}$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $3$:
$x = 4$
This answer corresponds to option $H$.
