1. **State the problem:** Solve the inequality $3^x + 1 > 1$ and the equation $3^x = 1$. 2. **Solve the inequality $3^x + 1 > 1$: ** Subtract 1 from both sides: $$3^x + 1 - 1 > 1 - 1$$ $$3^x > 0$$ Since $3^x$ is an exponential function with base 3 (which is positive and greater than 1), it is always positive for all real $x$. Therefore, the inequality holds for all real numbers. 3. **Solve the equation $3^x = 1$: ** Recall that any number to the power 0 is 1: $$3^0 = 1$$ Therefore, the solution is: $$x = 0$$ **Final answers:** - Inequality $3^x + 1 > 1$ is true for all real $x$. - Equation $3^x = 1$ has solution $x = 0$.