https://file.aiquickdraw.com/mathbot/file/172617612719874wkodqv.jpg

Let's solve the inequality \( 6 - 7y \leq 8y - 20 \).

### Step-by-step solution:

1. **Move all terms involving \( y \) to one side:**
   \[
   6 - 7y \leq 8y - 20
   \]
   Add \( 7y \) to both sides:
   \[
   6 \leq 15y - 20
   \]

2. **Move constant terms to the other side:**
   Add \( 20 \) to both sides:
   \[
   6 + 20 \leq 15y
   \]
   Simplifying:
   \[
   26 \leq 15y
   \]

3. **Solve for \( y \):**
   Divide both sides by \( 15 \):
   \[
   y \geq \frac{26}{15}
   \]

Thus, the solution is \( y \geq \frac{26}{15} \).

### Graphing the solution:

- On a number line, the point \( y = \frac{26}{15} \) is included (closed circle) since the inequality is \( \geq \), and we shade to the right because the inequality is "greater than."

Would you like to see a graph of this solution, or do you have any questions?

### Follow-up questions:
1. What happens if you multiply or divide by a negative number in an inequality?
2. How would the solution change if the inequality were strict, e.g., \( y > \frac{26}{15} \)?
3. Can inequalities have no solution? Under what conditions?
4. How can you solve inequalities that involve absolute values?
5. What are the differences between solving equations and inequalities?

#### Tip:
When graphing inequalities on a number line, always use an open circle for strict inequalities \( (<, >) \) and a closed circle for non-strict inequalities \( (\leq, \geq) \).

Solve and graph the solution set: 6 - 7y ≤ 8y - 20

Learn how to solve and graph the inequality 6 - 7y ≤ 8y - 20 with step-by-step instructions. Understand the key algebraic concepts, manipulation of inequalities, and graphing techniques. Suitable for students in Grades 8-10.

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