https://file.aiquickdraw.com/mathbot/file/1725837981561tkeyaird.jpg

Solve AND graph the Solution yo each of the inequalities

The inequality in the image appears to be:

\[
\frac{x}{3} \leq 1
\]

### Solving the inequality:

1. Multiply both sides of the inequality by 3 to eliminate the fraction:
   \[
   x \leq 3
   \]

Thus, the solution to the inequality is \( x \leq 3 \).

### Graphing the solution:

The solution \( x \leq 3 \) represents all values of \( x \) that are less than or equal to 3. On a number line, this would be represented as:

- A closed circle at \( x = 3 \) (indicating that \( x = 3 \) is included in the solution).
- A line extending to the left from \( x = 3 \) towards negative infinity (since all values less than 3 are included).

Would you like to see a detailed graph of this solution or have any specific questions about it?

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Here are 5 related questions for further exploration:
1. How would the solution change if the inequality was strict (i.e., \( \frac{x}{3} < 1 \))?
2. What is the effect of multiplying or dividing by a negative number in inequalities?
3. How would you represent \( x > 3 \) on a number line?
4. Can you solve and graph the inequality \( \frac{x}{3} \geq 1 \)?
5. How do inequalities differ from equations in terms of graphing?

**Tip:** When multiplying or dividing both sides of an inequality by a negative number, always remember to reverse the direction of the inequality.

Solve and graph the solution to each of the inequalities.

Learn how to solve the inequality \( \frac{x}{3} \leq 1 \) and graph the solution step-by-step. This problem demonstrates how to eliminate fractions in inequalities and how to represent solutions on a number line. Suitable for students in Grades 7-9.

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