Let's analyze the statement and its converse to determine if they form a biconditional that is true.

Original Statement:

"If $10k + 6 = -4$, then $k = -1$."

Step 1: Solve the original statement

Given the equation $10k + 6 = -4$, we can solve for $k$:

$10k + 6 = -4$

Subtract 6 from both sides:

$10k = -10$

Divide both sides by 10:

$k = -1$

This shows that the original statement is true.

Converse Statement:

The converse of the original statement is: "If $k = -1$, then $10k + 6 = -4$."

Step 2: Verify the converse

Substitute $k = -1$ into the equation $10k + 6$:

$10(-1) + 6 = -10 + 6 = -4$

The converse statement is also true.

Biconditional Statement:

A biconditional statement is true if both the original statement and its converse are true. In this case, both the original statement and its converse are true, so the biconditional statement:

$10k + 6 = -4 \text{ if and only if } k = -1$

is true.

Conclusion:

Yes, the original statement and its converse form a biconditional that is true.

Would you like any details or have further questions?

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Here are 5 related questions you might consider:

1. What is the general process for solving linear equations with one variable?
2. How can you determine the truth of a converse statement?
3. What are the conditions under which a biconditional statement is true?
4. How does solving a system of equations differ from solving a single equation?
5. What are some common mistakes to avoid when solving linear equations?

Tip: When verifying a converse statement, always substitute the value from the conclusion of the original statement back into the premise to check for consistency.