https://file.aiquickdraw.com/mathbot/file/17270159133818rovmaoa.jpg

The inequality presented in the image is:

\[
-2 \leq 2x < 6
\]

Let's solve this inequality step by step.

### Step 1: Divide the inequality by 2
Since all terms in the inequality involve \( 2x \), divide the entire inequality by 2:

\[
-2 \div 2 \leq 2x \div 2 < 6 \div 2
\]

This simplifies to:

\[
-1 \leq x < 3
\]

### Step 2: Interpret the solution
The solution is the set of real numbers \( x \) such that \( -1 \leq x < 3 \). In interval notation, this can be written as:

\[
[-1, 3)
\]

### Step 3: Match with the given options
Now, let's match this solution with the options:

- **a.** \( (-\infty, 3] \) — This is incorrect, since it includes all numbers less than or equal to 3, which is not the correct interval.
- **b.** \( \{x \in \mathbb{R} \mid -1 \leq x < 3\} \) — This is **correct**, as it represents exactly the same solution.
- **c.** \( [-3, \infty) \) — This is incorrect, since it includes numbers less than -1 and greater than 3.
- **d.** \( [-1, 3) \) — This is **correct**, as it is the interval form of the solution.
- **e.** \( \{x \in \mathbb{R} \mid -3 \leq x < 1\} \) — This is incorrect, as it defines a different range.

### Final Answer:
The correct options are **b** and **d**.

Let me know if you'd like further details or if you have any questions!

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Here are some related questions:
1. What is the difference between interval notation and set-builder notation?
2. How do you solve compound inequalities like this one?
3. Can the inequality symbols change direction when solving?
4. What does it mean for an interval to be "open" or "closed"?
5. How do you graph an inequality on a number line?

**Tip**: When dividing or multiplying inequalities by negative numbers, remember to reverse the inequality signs!

Himpunan semua bilangan real yang memenuhi pertidaksamaan −2 ≤ 2x < 6 adalah…

Learn how to solve the compound inequality −2 ≤ 2x < 6 and determine the solution set in both set notation and interval notation. This problem focuses on solving inequalities and interpreting the correct solution from multiple choices. Suitable for Grades 9-11.

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