Variable $x$ cannot be equal to $-\frac{2}{3}$ since division by zero is not defined. Multiply both sides of the equation by $2\left(3x+2\right)$, the least common multiple of $3x+2,2$.
$$2\left(2x-1\right)=31\left(3x+2\right)$$
Use the distributive property to multiply $2$ by $2x-1$.
$$4x-2=31\left(3x+2\right)$$
Use the distributive property to multiply $31$ by $3x+2$.
$$4x-2=93x+62$$
Subtract $93x$ from both sides.
$$4x-2-93x=62$$
Combine $4x$ and $-93x$ to get $-89x$.
$$-89x-2=62$$
Add $2$ to both sides.
$$-89x=62+2$$
Add $62$ and $2$ to get $64$.
$$-89x=64$$
Divide both sides by $-89$.
$$x=\frac{64}{-89}$$
Fraction $\frac{64}{-89}$ can be rewritten as $-\frac{64}{89}$ by extracting the negative sign.
