https://file.aiquickdraw.com/mathbot/file/17266758570885lf4bcm6.jpg

Let's evaluate the expressions that are equivalent to \(-5(2j)\).

1. Simplify \(-5(2j)\):
   \[
   -5(2j) = -10j
   \]

Now, let's evaluate the given options:

1. **\( j(-5 \cdot 2) \):**
   \[
   j(-5 \cdot 2) = j(-10) = -10j
   \]
   This is equivalent to \(-10j\), so it is correct.

2. **\( -10j \):**
   This is already \(-10j\), so it is correct.

3. **\( j - 10 \):**
   This simplifies to \( j - 10 \), which is not equivalent to \(-10j\). So, this is incorrect.

4. **\( -5(-4j + 6j) \):**
   Simplify the expression inside the parentheses:
   \[
   -4j + 6j = 2j
   \]
   Now, distribute the \(-5\):
   \[
   -5(2j) = -10j
   \]
   This is equivalent to \(-10j\), so it is correct.

### Conclusion:
The correct expressions that are equivalent to \(-5(2j)\) are:
- \( j(-5 \cdot 2) \)
- \( -10j \)
- \( -5(-4j + 6j) \)

Let me know if you'd like more details or have further questions.

Here are five related questions for practice:
1. What is the simplified form of \( -4(3x + 2x) \)?
2. How do you distribute negative numbers in expressions like \( -5(a + b) \)?
3. If \( -3(4y - 2z) \), what is the simplified expression?
4. How can you factor the expression \( 10j - 20k \)?
5. How do you simplify the expression \( -6(5 - 2j) \)?

**Tip:** When dealing with parentheses, always simplify inside first before applying any multiplication.

Select the expressions that are equivalent to -5(2j).

Explore the solution to identify expressions equivalent to -5(2j). This problem covers key algebraic concepts such as simplification and the distributive property, suitable for students in Grades 6-8.

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