1. Statement of the problem: MNOP is a parallelogram and two consecutive interior angles are $3x-1$ and $2x-1$. 2. In a parallelogram, consecutive angles are supplementary, so their measures add up to $180$ degrees. 3. Set up the equation using that fact: $(3x-1)+(2x-1)=180$. 4. Combine like terms on the left: $5x-2=180$. 5. Solve for $x$: add $2$ to both sides to get $5x=182$. 6. Divide both sides by $5$ to find $x=\frac{182}{5}$. 7. As a decimal, $x=36.4$. 8. Check the solution by substituting back: $3x-1=3\cdot\frac{182}{5}-1=\frac{546}{5}-1=\frac{541}{5}=108.2$. 9. Also $2x-1=2\cdot\frac{182}{5}-1=\frac{364}{5}-1=\frac{359}{5}=71.8$. 10. Their sum is $108.2+71.8=180$, so the solution is valid. 11. Final answer: $x=\frac{182}{5}=36.4$.