1. **State the problem:** Given the equation $$\sqrt{15} - 9x = 48$$, find the value of $$x$$. 2. **Rewrite the equation:** The problem states $$\sqrt{15} - 9x = 48$$. Note that $$\sqrt{15}$$ is a constant approximately equal to 3.873. 3. **Isolate the term with $$x$$:** Subtract $$\sqrt{15}$$ from both sides: $$-9x = 48 - \sqrt{15}$$ 4. **Divide both sides by $$-9$$ to solve for $$x$$:** $$x = \frac{48 - \sqrt{15}}{-9} = \frac{\cancel{48} - \cancel{\sqrt{15}}}{\cancel{-9}}$$ 5. **Simplify the expression:** $$x = -\frac{48 - \sqrt{15}}{9} = -\frac{48}{9} + \frac{\sqrt{15}}{9} = -\frac{16}{3} + \frac{\sqrt{15}}{9}$$ 6. **Approximate the value:** $$x \approx -5.333 + 0.430 = -4.903$$ **Final answer:** $$x = -\frac{16}{3} + \frac{\sqrt{15}}{9} \approx -4.903$$