To graph the solution of the inequality $5x - 4 \geq 2x + 11$, we follow these steps:

Step 1: Solve the Inequality

We already solved the inequality and found: $x \geq 5$

Step 2: Graphing on a Number Line

1. Draw a number line: Start by drawing a horizontal line and marking relevant points, especially $x = 5$.

2. Plot the solution $x \geq 5$:

   • Closed circle at $x = 5$: Since the inequality is $\geq$, we include $x = 5$ in the solution, so place a solid (closed) circle on the number line at $x = 5$.
   • Shade the region to the right of 5: The inequality $x \geq 5$ means that all values greater than or equal to 5 satisfy the inequality. So, shade the line to the right of the point $x = 5$ to indicate all these values.

Here's what the graph should look like:

• The number line will have a solid circle at 5, with a shaded line extending to the right, indicating that the solution includes all numbers greater than or equal to 5.

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Would you like further details or have any questions?

Here are 5 related questions:

1. How would the graph change if the inequality were $x > 5$ instead of $x \geq 5$?
2. Can you describe what the graph would look like for $x \leq 5$?
3. How do you graph inequalities on a coordinate plane?
4. What happens if we have a compound inequality like $3 \leq x < 7$?
5. What is the importance of the type of circle (open or closed) in inequality graphs?

Tip: Always double-check if the circle should be open or closed based on whether the inequality includes the value ( $\geq$ or $\leq$ for closed circles, $>$ or $<$ for open circles).