The sum of the opposite of a number and the absolute value of the number is equal to the number itself.True,sometimes true,never true?

-N+abs(N)=N ?

abs(N)=2N ?

Nope, never true, at least in Texas

but zero?

Professor Damon is correct. We think big in Texas, and zero is seldom encountered.

To determine whether the statement is true, sometimes true, or never true, let's break it down.

The statement is: "The sum of the opposite of a number and the absolute value of the number is equal to the number itself."

Let's represent the number as "x" for simplicity.

The opposite of a number x is represented as -x.
The absolute value of a number x is denoted as |x|.

According to the statement, the sum of the opposite of x (-x) and the absolute value of x (|x|) should be equal to x itself.

So, mathematically, the statement can be written as:
(-x) + |x| = x

To determine if this equation is true, sometimes true, or never true, we can consider different scenarios:

1. If x is a positive number:
For example, let's assume x = 5.
(-5) + |5| = 5
-5 + 5 = 5
0 = 5
This equation is never true when x is a positive number, as 0 is not equal to 5.

2. If x is a negative number:
For example, let's assume x = -3.
-(-3) + |-3| = -3
3 + 3 = -3
6 = -3
This equation is never true when x is a negative number, as 6 is not equal to -3.

3. If x is zero:
For example, let's assume x = 0.
-(0) + |0| = 0
0 + 0 = 0
0 = 0
This equation is always true when x is zero, as 0 is equal to 0.

Based on these scenarios, we can conclude that the statement is sometimes true, but not always true.