Solve the inequality and graph the solution on the line provided.
minus, 2, x, minus, 4, is greater than, 10
−2x−4>
10

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?

---

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.

Solve the inequality and graph the solution on the line provided: −2x−4 > 10

Learn how to solve the linear inequality −2x−4 > 10 step-by-step, including the reversal of inequality when dividing by a negative number. Graph the solution on a number line and understand key concepts in linear inequalities. Suitable for students in Grades 8-10.

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