1. **State the problem:** We have a triangle with angles 73° and 33°, and sides opposite these angles labeled as $2x - 1$ and $x$ respectively. We need to find the value of $x$ to the nearest tenth. 2. **Recall the Law of Sines:** For any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 3. **Apply the Law of Sines to the given triangle:** Let side $a = 2x - 1$ opposite angle $A = 73^\circ$, and side $b = x$ opposite angle $B = 33^\circ$. Set up the ratio: $$\frac{2x - 1}{\sin 73^\circ} = \frac{x}{\sin 33^\circ}$$ 4. **Cross multiply to solve for $x$:** $$ (2x - 1) \sin 33^\circ = x \sin 73^\circ $$ 5. **Distribute and rearrange:** $$ 2x \sin 33^\circ - \sin 33^\circ = x \sin 73^\circ $$ 6. **Group $x$ terms on one side:** $$ 2x \sin 33^\circ - x \sin 73^\circ = \sin 33^\circ $$ 7. **Factor out $x$:** $$ x (2 \sin 33^\circ - \sin 73^\circ) = \sin 33^\circ $$ 8. **Solve for $x$:** $$ x = \frac{\sin 33^\circ}{2 \sin 33^\circ - \sin 73^\circ} $$ 9. **Calculate the sine values:** $$ \sin 33^\circ \approx 0.5446, \quad \sin 73^\circ \approx 0.9563 $$ 10. **Substitute and simplify:** $$ x = \frac{0.5446}{2 \times 0.5446 - 0.9563} = \frac{0.5446}{1.0892 - 0.9563} = \frac{0.5446}{0.1329} $$ 11. **Final calculation:** $$ x \approx 4.096 $$ 12. **Round to the nearest tenth:** $$ x \approx 4.1 $$ **Answer:** The value of $x$ to the nearest tenth is **4.1**.