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To solve the inequality \( x + 8 \geq 2 \):

### Part (a)
1. Start by isolating \( x \) on one side of the inequality:
   \[
   x + 8 \geq 2
   \]

2. Subtract 8 from both sides to solve for \( x \):
   \[
   x \geq 2 - 8
   \]
   \[
   x \geq -6
   \]

So, the solution to the inequality is:
\[
x \geq -6
\]

### Part (b)
To represent this on a number line:
- Draw a line and mark a point at \( -6 \).
- Use a closed (filled) circle at \( -6 \) to indicate that \( -6 \) is included in the solution (since it’s \( \geq \)).
- Shade the line to the right of \( -6 \) to represent all values greater than or equal to \( -6 \).

Would you like a more detailed explanation, or do you have any questions about this solution?

### Additional Questions for Practice:
1. How would the solution change if the inequality were \( x + 8 > 2 \)?
2. What would the solution look like if the inequality were \( x + 8 \leq 2 \)?
3. How can you represent the solution on a number line if the inequality were \( x < -6 \)?
4. What steps would you follow if the inequality involved a multiplication, like \( 2x + 8 \geq 2 \)?
5. How would you solve and represent \( x - 4 \geq 0 \) on a number line?

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

Solve the inequality x + 8 ≥ 2 and draw the solution on a number line.

Understand how to solve the inequality x + 8 ≥ 2 and represent the solution on a number line. This guide includes algebraic steps to isolate x and tips for graphing inequalities. Ideal for students in Grades 7-9.

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