Solve the inequality and graph the solution on the line provided.
7, x, minus, 2, is greater than or equal to, 12
7x−2≥
12

To solve the inequality \(7x - 2 \geq 12\), follow these steps:

1. **Add 2 to both sides** of the inequality to isolate the term with \(x\):
   \[
   7x - 2 + 2 \geq 12 + 2
   \]
   Simplifies to:
   \[
   7x \geq 14
   \]

2. **Divide both sides by 7** to solve for \(x\):
   \[
   \frac{7x}{7} \geq \frac{14}{7}
   \]
   Simplifies to:
   \[
   x \geq 2
   \]

### Solution:
The solution to the inequality is \(x \geq 2\).

### Graphing the Solution on the Number Line:

1. Draw a number line.
2. Mark the point \(2\) on the number line.
3. Since \(x\) is greater than or equal to \(2\), draw a solid circle at \(2\) to indicate that \(2\) is included in the solution.
4. Shade the number line to the right of \(2\) to represent all numbers greater than or equal to \(2\).

Would you like a detailed explanation of any part, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the solution change if the inequality were \(7x - 2 > 12\)?
2. What would happen if the inequality had a negative coefficient for \(x\)?
3. How do you solve the inequality \(7x - 2 \leq 12\)?
4. What is the solution to \(7x - 2 = 12\) (an equation rather than an inequality)?
5. How do you graph inequalities with multiple conditions, like \(x \geq 2\) and \(x < 5\)?

**Tip:** When solving inequalities, if you multiply or divide both sides by a negative number, remember to reverse the inequality sign.

Learn how to solve the inequality 7x - 2 ≥ 12 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear inequalities and graphing solutions on a number line. Suitable for students in Grades 7-9.

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