To match the expressions on the left with their simplified forms on the right, let's go through each expression one by one:
1. -(-6): The expression -(-6) can be simplified by applying the double negative rule, which states that two negatives cancel each other out and become a positive. Therefore, -(-6) simplifies to 6.
2. | -6 |: The expression | -6 | represents the absolute value of -6. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. In this case, |-6| simplifies to 6.
3. - | 6 |: The expression - | 6 | represents the negative of the absolute value of 6. Since the absolute value of 6 is 6, taking the negative of it gives us -6.
4. | 6 |: The expression | 6 | represents the absolute value of 6, which is simply 6. Therefore, | 6 | simplifies to 6.
5. - 6: The expression - 6 represents the negative of 6. Taking the negative of a positive number results in a negative value, so - 6 remains as -6.
6. |-(-6)|: The expression |-(-6)| can be simplified by first applying the double negative rule to get |-(-6)| = |6|. Then, using the absolute value rule, we know that the absolute value of any positive or zero number is itself. Therefore, |-(-6)| simplifies to 6.
So, matching the expressions on the left with their simplified forms on the right:
-(-6) = 6
|-6| = 6
-|6| = -6
|6| = 6
-6 = -6
|-(-6)| = 6
Explanation: