To solve the equation [tex]\( |w| + 14 = 20 \)[/tex], let's follow these steps:
1. Isolate the absolute value: Start by isolating the [tex]\( |w| \)[/tex] term on one side of the equation.
[tex]\[
|w| + 14 = 20
\][/tex]
Subtract 14 from both sides to isolate [tex]\( |w| \)[/tex]:
[tex]\[
|w| = 20 - 14
\][/tex]
[tex]\[
|w| = 6
\][/tex]
2. Solve the absolute value equation: Recall that the absolute value [tex]\( |w| \)[/tex] represents the distance of [tex]\( w \)[/tex] from 0 on the number line, which means:
[tex]\[
|w| = 6 \implies w = 6 \quad \text{or} \quad w = -6
\][/tex]
Therefore, the solutions to the equation [tex]\( |w| + 14 = 20 \)[/tex] are [tex]\( w = 6 \)[/tex] and [tex]\( w = -6 \)[/tex].
Thus, the solutions are [tex]\( w = 6, -6 \)[/tex].
