In the following expression, n is a rational number:
-0.7(n+(-n))
Which expression below is equivalent to this expression?
A. -n(-0.7 +(-0.7))
B. 0.7n + 0.7n
C. -0.7n -0.7n
D. - 0.7 * n + (-0.7) *
(-n)
Answer: D. - 0.7 * n + (-0.7) * (-n)
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-0.7(n+(-n))
= -.7(n - n)
= -.7(0)
= 0
To determine which expression is equivalent to -0.7(n+(-n)), let's simplify the given expression step by step:
First, let's consider the part inside the parentheses: n+(-n). Adding n and the additive inverse of n (-n) will result in zero. So, n+(-n) simplifies to zero.
Next, we substitute the simplified expression back into the original expression: -0.7(0).
Anything multiplied by zero is zero. Therefore, the original expression -0.7(n+(-n)) simplifies to zero.
Now, let's analyze the answer choices:
A. -n(-0.7 + (-0.7))
This expression expands to -n(-1.4), which simplifies to 1.4n. Since this is not equivalent to zero, option A is not correct.
B. 0.7n + 0.7n
This expression combines like terms, resulting in 1.4n. As mentioned above, this expression is not equivalent to zero, so option B is not correct either.
C. -0.7n - 0.7n
This expression also combines like terms, resulting in -1.4n. Similar to the previous choices, this expression is not equivalent to zero. Thus, option C is not correct.
D. -0.7 * n + (-0.7) *
This expression doesn't provide a complete equation; therefore, we cannot determine its value or equivalence.
Since none of the available answer choices result in zero, none of them are equivalent to the original expression -0.7(n+(-n)).