5x - 4 is greater than or equal to 2x + 11. Enter the simplified inequality in the box.

Solve the inequality and graph the solution.

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.

Learn how to solve the inequality 5x - 4 ≥ 2x + 11 with a detailed step-by-step solution. This problem covers key algebraic concepts related to inequalities. Suitable for students in Grades 7-9.

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