To determine the value(s) for [tex]\( n \)[/tex] that satisfy the equation [tex]\( |n| = 3.5 \)[/tex], let's go through the steps:
1. Understanding the Absolute Value:
The absolute value of a number [tex]\( n \)[/tex], denoted as [tex]\( |n| \)[/tex], is defined as the non-negative value of [tex]\( n \)[/tex] without regard to its sign. Therefore, [tex]\( |n| = n \)[/tex] if [tex]\( n \geq 0 \)[/tex] and [tex]\( |n| = -n \)[/tex] if [tex]\( n < 0 \)[/tex].
2. Interpreting the Given Equation:
The equation [tex]\( |n| = 3.5 \)[/tex] tells us that the absolute value of [tex]\( n \)[/tex] is 3.5. This means that [tex]\( n \)[/tex] can be either positive 3.5 or negative 3.5 to satisfy the equation.
3. Finding the Solutions:
Considering the absolute value definition, we get two possible solutions:
- If [tex]\( n \geq 0 \)[/tex], [tex]\( |n| = n \)[/tex]. So, [tex]\( n = 3.5 \)[/tex].
- If [tex]\( n < 0 \)[/tex], [tex]\( |n| = -n \)[/tex]. So, [tex]\( -n = 3.5 \)[/tex], which implies [tex]\( n = -3.5 \)[/tex].
4. Listing the Solutions:
Thus, the solutions to the equation [tex]\( |n| = 3.5 \)[/tex] are [tex]\( n = 3.5 \)[/tex] and [tex]\( n = -3.5 \)[/tex].
In summary, the values for [tex]\( n \)[/tex] that make the expression [tex]\( |n| = 3.5 \)[/tex] true are 3.5 and -3.5.
Therefore, the correct answer is:
[tex]\[ 3.5 \text{ and } -3.5 \][/tex]
