Variable $x$ cannot be equal to $\frac{2}{3}$ since division by zero is not defined. Multiply both sides of the equation by $9\left(3x-2\right)$, the least common multiple of $3x-2,9$.
$$9\left(2x+1\right)=5\left(3x-2\right)$$
Use the distributive property to multiply $9$ by $2x+1$.
$$18x+9=5\left(3x-2\right)$$
Use the distributive property to multiply $5$ by $3x-2$.
$$18x+9=15x-10$$
Subtract $15x$ from both sides.
$$18x+9-15x=-10$$
Combine $18x$ and $-15x$ to get $3x$.
$$3x+9=-10$$
Subtract $9$ from both sides.
$$3x=-10-9$$
Subtract $9$ from $-10$ to get $-19$.
$$3x=-19$$
Divide both sides by $3$.
$$x=\frac{-19}{3}$$
Fraction $\frac{-19}{3}$ can be rewritten as $-\frac{19}{3}$ by extracting the negative sign.
