Solve for [tex]w[/tex].

[tex]\[ |w| + 14 = 20 \][/tex]

If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

[tex]\[ w = \][/tex]
[tex]\[ \square \][/tex]
[tex]\[ \text{No solution} \][/tex]



Answer :

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].