1. **State the problem:** Solve the inequality $$5(x + 2) \geq 3x + 14$$. 2. **Apply the distributive property:** Multiply 5 by both terms inside the parentheses. $$5x + 10 \geq 3x + 14$$ 3. **Isolate variable terms on one side:** Subtract $$3x$$ from both sides. $$5x + 10 - 3x \geq 3x + 14 - 3x$$ Intermediate step showing cancellation: $$\cancel{5x} + 10 - \cancel{3x} \geq \cancel{3x} + 14 - \cancel{3x} \Rightarrow 2x + 10 \geq 14$$ 4. **Isolate the variable term:** Subtract 10 from both sides. $$2x + 10 - 10 \geq 14 - 10$$ Intermediate step showing cancellation: $$2x + \cancel{10} - \cancel{10} \geq 14 - 10 \Rightarrow 2x \geq 4$$ 5. **Solve for $$x$$:** Divide both sides by 2. $$\frac{2x}{2} \geq \frac{4}{2}$$ Intermediate step showing cancellation: $$\frac{\cancel{2}x}{\cancel{2}} \geq \frac{4}{2} \Rightarrow x \geq 2$$ 6. **Final answer:** $$x \geq 2$$. This means any value of $$x$$ greater than or equal to 2 satisfies the inequality.