1. **State the problem:** Solve the equation $$3 \tan x = -4$$ for $$0^\circ \leq x \leq 360^\circ$$. 2. **Isolate $$\tan x$$:** Divide both sides by 3: $$3 \tan x = -4 \implies \tan x = \frac{-4}{3}$$ 3. **Recall the tangent function properties:** - Tangent is negative in the second and fourth quadrants. - The general solution for $$\tan x = t$$ is $$x = \arctan(t) + k \times 180^\circ$$ for any integer $$k$$. 4. **Find the reference angle:** $$\theta = \arctan\left(\left|\frac{4}{3}\right|\right) = \arctan\left(\frac{4}{3}\right) \approx 53.13^\circ$$ 5. **Find solutions in the specified interval:** - In the second quadrant: $$x = 180^\circ - 53.13^\circ = 126.87^\circ$$ - In the fourth quadrant: $$x = 360^\circ - 53.13^\circ = 306.87^\circ$$ 6. **Final answer:** $$x = 126.87^\circ \quad \text{or} \quad x = 306.87^\circ$$