1. **State the problem:** Solve the inequality $$1 - (x(t))^2 \geq \frac{8}{3}$$ for $x(t)$.\n\n2. **Rewrite the inequality:** Move all terms to one side to isolate the quadratic term:\n$$1 - (x(t))^2 \geq \frac{8}{3} \implies 1 - (x(t))^2 - \frac{8}{3} \geq 0$$\n\n3. **Combine constants:** Convert 1 to a fraction with denominator 3 to combine:\n$$\frac{3}{3} - (x(t))^2 - \frac{8}{3} \geq 0 \implies - (x(t))^2 + \frac{3}{3} - \frac{8}{3} \geq 0$$\n$$- (x(t))^2 - \frac{5}{3} \geq 0$$\n\n4. **Rewrite inequality:**\n$$- (x(t))^2 \geq \frac{5}{3}$$\n\n5. **Multiply both sides by -1:** Remember to reverse the inequality sign when multiplying by a negative number:\n$$\cancel{-1} \cdot - (x(t))^2 \leq \cancel{-1} \cdot \frac{5}{3} \implies (x(t))^2 \leq -\frac{5}{3}$$\n\n6. **Analyze the inequality:** The square of a real number $(x(t))^2$ is always greater than or equal to 0, but the right side is negative $-\frac{5}{3}$.\n\n7. **Conclusion:** Since $(x(t))^2 \leq$ a negative number is impossible for real $x(t)$, there is **no real solution** to the inequality.\n\n**Final answer:** No real values of $x(t)$ satisfy the inequality $$1 - (x(t))^2 \geq \frac{8}{3}$$.