To solve for [tex]\( j \)[/tex] in the equation [tex]\( 0 = 5|j| \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
0 = 5|j|
\][/tex]
2. Isolate the absolute value of [tex]\( j \)[/tex]:
Divide both sides of the equation by 5 to isolate [tex]\( |j| \)[/tex]:
[tex]\[
\frac{0}{5} = \frac{5|j|}{5}
\][/tex]
Simplifying this, we get:
[tex]\[
0 = |j|
\][/tex]
3. Interpret the absolute value expression:
The absolute value of [tex]\( j \)[/tex] is the non-negative value of [tex]\( j \)[/tex]. Since [tex]\( |j| \)[/tex] represents the distance of [tex]\( j \)[/tex] from 0 on the number line, if [tex]\( |j| = 0 \)[/tex], then [tex]\( j \)[/tex] must be 0.
4. Solve for [tex]\( j \)[/tex]:
Hence,
[tex]\[
j = 0
\][/tex]
Thus, the solution to the equation [tex]\( 0 = 5|j| \)[/tex] is [tex]\( j = 0 \)[/tex].
