Q46. - Algebra 1

Question

For what values of n is the opposite of n greater than n? For what values of n is the opposite of n less than n? For what values is n equal to its opposite?

Step-by-Step Solution

Answer

The opposite $n$ is greater than $n$ when $n<0$, lesser than $n$ when, $n>0$ and equal to $n$ when $n=0$.

Step 1. State the concept.

The opposite of $n$ is $-n$.

Step 2. Condition 1.

Let $-n$ be greater than $n$.

Then,

$\begin{array}{l}-n>n\\ 0>2n\\ 2n<0\\ n<0\end{array}$

So, the opposite of $n$ is greater than $n$ when $n<0$.

Step 3. Condition 2.

Let $-n$ be lesser than $n$.

Then,

$\begin{array}{l}-n<n\\ 0<2n\\ 2n>0\\ n>0\end{array}$

So, the opposite of $n$ is lesser than $n$ when $n>0$.

Step 4. Condition 3.

Let's $-n$ be equal to $n$.

Then,

$\begin{array}{l}-n=n\\ 0=2n\\ 2n=0\\ n=0\end{array}$

So, the opposite $n$ is equal to $n$ when $n=0$.

Thus, the opposite $n$ is greater than $n$ when $n<0$, lesser than $n$ when, $n>0$ and equal to $n$ when $n=0$.