All of the following have the same value except _____.
9 + (-6)
6 - 9
9 - 6
-6 - (-9)
9 + (-6)
To determine which expressions have the same value, we can evaluate each expression step-by-step:
1. 9 + (-6):
- The subtraction operation can be thought of as adding the additive inverse.
- (-6) is the additive inverse of 6, so 9 + (-6) is equivalent to 9 - 6.
- Therefore, 9 + (-6) is equivalent to 9 - 6.
2. 6 - 9:
- Subtracting 9 from 6 gives a negative result.
- Therefore, 6 - 9 is not equivalent to 9 + (-6) or 9 - 6.
3. 9 - 6:
- Subtracting 6 from 9 gives a positive result.
- Therefore, 9 - 6 is not equivalent to 9 + (-6) or 6 - 9.
4. -6 - (-9):
- Subtracting a negative number is equivalent to adding its positive counterpart.
- To subtract -(-9), we can rewrite it as -1 * (-9), which is equal to 9.
- Therefore, -6 - (-9) is equivalent to -6 + 9.
In summary, the expressions that have the same value are 9 + (-6) and 9 - 6, as they both equal 3. The expression 6 - 9 and -6 - (-9) have different values.