Let's solve the inequality step by step.

Given Inequality:

$5x - 4 \geq 2x + 11$

Step 1: Subtract $2x$ from both sides to get all the terms involving $x$ on one side.

$5x - 2x - 4 \geq 11$ $3x - 4 \geq 11$

Step 2: Add 4 to both sides to isolate the term with $x$.

$3x \geq 11 + 4$ $3x \geq 15$

Step 3: Divide both sides by 3 to solve for $x$.

$x \geq \frac{15}{3}$ $x \geq 5$

Final Answer:

The simplified inequality is $x \geq 5$.

Graphing the Solution:

On a number line, plot a closed circle at $x = 5$ (because $\geq$ includes 5), and shade the region to the right of 5 to represent all numbers greater than or equal to 5.

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Do you want more details or have any questions?

Here are 5 related questions:

1. How would the inequality change if the original expression were $5x - 4 > 2x + 11$?
2. How do you graph the solution if the inequality is $x > 5$ instead of $x \geq 5$?
3. What would the solution be if the inequality was $5x - 4 \leq 2x + 11$?
4. How can you check if your solution to the inequality is correct?
5. How does solving inequalities differ from solving equations?

Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.