We are tasked with solving the inequality:

$-2x - 4 > 10$

Step-by-step solution:

1. Add 4 to both sides: $-2x - 4 + 4 > 10 + 4$ $-2x > 14$

2. Divide both sides by -2: When dividing by a negative number, we must reverse the inequality sign. $\frac{-2x}{-2} < \frac{14}{-2}$ $x < -7$

So, the solution is: $x < -7$

Graphing the solution on a number line:

• Draw a number line.
• Place an open circle at $x = -7$ because $-7$ is not included in the solution (since the inequality is strict: $<$).
• Shade the line to the left of $-7$, indicating that $x$ can be any number less than $-7$.

Would you like me to generate a graph of the solution?

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Here are 5 related questions for practice:

1. Solve $3x + 5 > 14$.
2. Solve $-x + 3 \leq 7$.
3. What happens when you multiply or divide by a negative number in an inequality?
4. Solve and graph $5 - 2x \leq 9$.
5. How would you solve $4x - 2 > 2x + 8$?

Tip: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.