https://file.aiquickdraw.com/mathbot/file/1727219102093f2rpnhvz.jpg

Let's solve the given inequality step-by-step.

### Inequality: 
\[
-7x \leq 2
\]

#### Step 1: Isolate \(x\)
To solve for \(x\), divide both sides of the inequality by \(-7\). Remember, when dividing by a negative number, the inequality sign flips:

\[
x \geq \frac{2}{-7}
\]

\[
x \geq -\frac{2}{7}
\]

#### Solution:
\[
x \geq -\frac{2}{7}
\]

#### Graph Representation:
To graph this inequality on a number line:
- You would place a closed circle at \(-\frac{2}{7}\) since it includes equality (≥).
- Then, shade the line to the right, indicating that the solution includes all values greater than \(-\frac{2}{7}\).

The graph in your image shows a closed circle and a line pointing to the right, which is correct for this inequality.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you solve inequalities involving absolute values?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. Can you explain how to graph compound inequalities?
4. How do you solve systems of inequalities graphically?
5. What are the differences between solving linear equations and inequalities?

### Tip:
Always remember that when you multiply or divide both sides of an inequality by a negative number, the inequality sign must flip!

Solve and graph the following inequality: -7x ≤ 2

Learn how to solve and graph the inequality -7x ≤ 2. This step-by-step solution covers key algebraic concepts, including the rules for dividing inequalities by negative numbers and graphing the solution on a number line. Ideal for students in Grades 7-9.

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