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.