Question

Check the following expressions. Use additive inverses and their properties to find the equivalent expressions:

-6 - 3
-6 + (-3)
6 - (-3)
-6 + 3
-6 - (-3)
6 + 3
6 - 3
6 + (-3)

Please verify the equivalent expressions for each and confirm.

Answer 1

The question involves finding equivalent expressions using additive inverses. The expressions are simplified using the rules of addition and subtraction, with special attention to the rules for subtracting negatives, resulting in expressions like -6 - 3 being equivalent to -9, and 6 - (-3) equivalent to 9.

Step-by-step explanation:

The expressions provided involve additive inverses and their properties. To find equivalent expressions, we use the rules for addition and subtraction of integers, including the subtraction of a negative resulting in addition.

• -6 - 3 is equivalent to -6 + (-3), both yielding -9.
• 6 - (-3) changes to 6 + 3 because subtracting a negative is the same as adding the positive counterpart. Thus, the expression is 9.
• -6 + 3 reflects adding a smaller positive number to a larger negative number, resulting in -3.
• -6 - (-3) turns into -6 + 3 because subtracting a negative is like adding its additive inverse, giving -3.
• 6 + 3 is a straightforward addition of two positive numbers, resulting in 9.
• 6 - 3 is simply subtracting a smaller positive number from a larger, resulting in 3.
• 6 + (-3) involves adding a negative to a positive, which is the same as subtracting the absolute value of the negative, yielding 3.