Solve the inequality and graph the solution on the line provided.

8, x, minus, 4, is greater than or equal to, minus, 68

8*x*−4≥

−68

To solve the inequality:

\[ 8x - 4 \geq -68 \]

### Step 1: Add 4 to both sides of the inequality.

\[
8x - 4 + 4 \geq -68 + 4
\]

\[
8x \geq -64
\]

### Step 2: Divide both sides by 8 to isolate \( x \).

\[
x \geq \frac{-64}{8}
\]

\[
x \geq -8
\]

### Solution: 
The solution to the inequality is:

\[
x \geq -8
\]

### Graphing on a number line:
- Draw a number line.
- Place a closed circle at \( x = -8 \) (since \( x \) is greater than or equal to -8).
- Shade the number line to the right of -8, indicating that \( x \) can take any value greater than or equal to -8.

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Do you want the graph drawn or any further details?

Here are 5 related questions to explore:
1. What happens if the inequality symbol changes to \( < \)?
2. How would the solution change if you added 5 to both sides first?
3. Can you rewrite the inequality as an equation and solve it?
4. What would the solution look like if you multiplied both sides by a negative number?
5. How do you check if your solution to the inequality is correct?

**Tip:** Always remember to reverse the inequality when multiplying or dividing by a negative number!

Solve the inequality and graph the solution on the line provided: 8x - 4 ≥ -68

Learn how to solve the inequality 8x - 4 ≥ -68 and graph the solution on a number line. This solution demonstrates key algebraic concepts such as adding to both sides and dividing an inequality. Suitable for students in Grades 6-8.

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