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It looks like you've uploaded an image related to a math problem. The image shows a graph and the inequality \(x^2 - 7 \leq 2x\).

To solve this inequality and graph it:

1. **Rewrite the Inequality**: 
   \[
   x^2 - 7 \leq 2x
   \]
   Subtract \(2x\) from both sides:
   \[
   x^2 - 2x - 7 \leq 0
   \]
   
2. **Find the Roots**: 
   To solve \(x^2 - 2x - 7 = 0\), use the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \(a = 1\), \(b = -2\), and \(c = -7\).
   \[
   x = \frac{2 \pm \sqrt{4 + 28}}{2}
   \]
   \[
   x = \frac{2 \pm \sqrt{32}}{2} = \frac{2 \pm 4\sqrt{2}}{2} = 1 \pm 2\sqrt{2}
   \]
   So, the roots are \(x = 1 + 2\sqrt{2}\) and \(x = 1 - 2\sqrt{2}\).

3. **Test Intervals**: 
   The critical points divide the number line into intervals:
   - \( (-\infty, 1 - 2\sqrt{2}) \)
   - \( (1 - 2\sqrt{2}, 1 + 2\sqrt{2}) \)
   - \( (1 + 2\sqrt{2}, \infty) \)

   Test a point in each interval to determine where the inequality is true.

4. **Graph**: 
   - The solutions to the inequality are the intervals where the inequality is less than or equal to zero.
   - These are the values of \(x\) where the parabola is below or touching the x-axis.
   
   For \(x^2 - 2x - 7 \leq 0\), the interval is between \(x = 1 - 2\sqrt{2}\) and \(x = 1 + 2\sqrt{2}\), inclusive.

Would you like more details on any of these steps? Here are some related questions that might be of interest:

1. How do you graph the solution to a quadratic inequality?
2. Can the quadratic formula be used for non-integer roots?
3. What is the significance of the discriminant in solving quadratic equations?
4. How do you test intervals when solving inequalities?
5. What does it mean for a solution to be "inclusive"?

**Tip:** Always check your solutions by plugging them back into the original inequality to ensure they satisfy the condition.

Graph the solution set of the inequality x^2 - 7 ≤ 2x.

Learn how to graph the solution set for the quadratic inequality x^2 - 7 ≤ 2x. This guide provides a step-by-step solution, covering key algebraic concepts like quadratic equations and inequalities. Suitable for high school students in Grades 9-12.

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