Solve the inequality and graph the solution on the line provided.
minus, 9, plus, 6, x, is greater than or equal to, 39
−9+6x≥
39

Let's solve the inequality step by step:

### Given inequality:
\[
-9 + 6x \geq 39
\]

### Step 1: Add 9 to both sides to eliminate the constant term on the left-hand side:
\[
-9 + 6x + 9 \geq 39 + 9
\]
\[
6x \geq 48
\]

### Step 2: Divide both sides by 6 to isolate \( x \):
\[
x \geq \frac{48}{6}
\]
\[
x \geq 8
\]

### Final solution:
\[
x \geq 8
\]

### Graphing the solution:
To graph this inequality on a number line:
1. Draw a number line and mark the point \( x = 8 \).
2. Since the inequality includes "greater than or equal to" ( \( \geq \) ), put a closed circle at \( x = 8 \) to indicate that \( x = 8 \) is included in the solution.
3. Shade the line to the right of 8 to show that \( x \) can take any value greater than or equal to 8.

Would you like a detailed graph of this solution?

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Here are 5 related questions to further explore this concept:
1. How would the graph change if the inequality were \( x > 8 \) instead of \( x \geq 8 \)?
2. How would you solve an inequality like \( 5x - 12 \leq 28 \)?
3. What is the difference between an open circle and a closed circle on a number line graph?
4. Can inequalities have more than one solution? How would you graph that?
5. How would you solve the inequality \( -3x + 7 > 25 \)?

**Tip:** Always remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality symbol.

Solve the inequality and graph the solution on the line provided: −9 + 6x ≥ 39.

Learn how to solve the linear inequality −9 + 6x ≥ 39 and graph the solution on a number line. This step-by-step guide covers key algebraic concepts, including linear inequalities and graphing, suitable for students in Grades 7-9.

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