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To rewrite the double inequality \(-3 < 3x < 15\) in its basic form, we need to isolate \(x\).

### Step-by-Step Solution:
1. **Start with the inequality**:
   \[
   -3 < 3x < 15
   \]

2. **Divide all parts by 3** to solve for \(x\):
   \[
   \frac{-3}{3} < \frac{3x}{3} < \frac{15}{3}
   \]

3. Simplify each term:
   \[
   -1 < x < 5
   \]

### Solution:
The inequality in its simplest form is:
\[
-1 < x < 5
\]

So, \(x\) lies between \(-1\) and \(5\).

Would you like more details on the steps? Or do you have any questions?

Here are five related questions for further exploration:
1. How would you graph the solution \(-1 < x < 5\) on a number line?
2. What is the solution set in interval notation?
3. How do you solve an inequality with a variable on both sides?
4. Can a double inequality involve non-linear expressions?
5. What are the differences between a strict inequality and a non-strict inequality?

**Tip:** When dividing or multiplying inequalities by a negative number, remember to reverse the inequality signs.

Rewrite the double inequality in its basic form: -3 < 3x < 15.

Learn how to solve the double inequality -3 < 3x < 15 by isolating x. Follow the step-by-step solution, which involves dividing each part of the inequality by 3, resulting in -1 < x < 5. Suitable for students in Grades 7-9.

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