1. **State the problem:** Solve the inequality $$-35 < 15 + 10p \geq 25$$. 2. **Understand the compound inequality:** This means two inequalities must hold simultaneously: - $$-35 < 15 + 10p$$ - $$15 + 10p \geq 25$$ 3. **Solve the first inequality:** $$-35 < 15 + 10p$$ Subtract 15 from both sides: $$-35 - 15 < 10p$$ $$-50 < 10p$$ Divide both sides by 10: $$\frac{-50}{\cancel{10}} < \frac{10p}{\cancel{10}}$$ $$-5 < p$$ 4. **Solve the second inequality:** $$15 + 10p \geq 25$$ Subtract 15 from both sides: $$10p \geq 25 - 15$$ $$10p \geq 10$$ Divide both sides by 10: $$\frac{10p}{\cancel{10}} \geq \frac{10}{\cancel{10}}$$ $$p \geq 1$$ 5. **Combine the results:** From the first inequality, $$p > -5$$. From the second inequality, $$p \geq 1$$. Since both must be true, the solution is: $$p \geq 1$$. **Final answer:** $$p \geq 1$$