Question: Solve the inequality $9 - 7x > 15$ Answer: $x$ [ ] [ ]
Instructions: Enter either $<$, $>$, $\geq$ or $\leq$ in the first answer box. Enter a number in the second answer box.
Note: In order to get credit for this problem all answers must be correct.
1. **State the problem:** Solve the inequality $$9 - 7x > 15$$
2. **Isolate the variable term:** Subtract 9 from both sides:
$$9 - 7x - 9 > 15 - 9$$
$$-7x > 6$$
3. **Divide both sides by $-7$ to solve for $x$:**
Remember, dividing by a negative number reverses the inequality sign.
$$\frac{-7x}{-7} < \frac{6}{-7}$$
$$x < -\frac{6}{7}$$
4. **Final answer:**
$$x < -\frac{6}{7}$$
This means $x$ is less than $-\frac{6}{7}$.
**Summary:** When dividing or multiplying an inequality by a negative number, the inequality sign flips. Here, dividing by $-7$ flipped $>$ to $<$.