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------------------------------------------------ Solve for [tex]$f$[/tex].

[tex]$62 = |f + 4|$[/tex]

Write your answers as integers or as proper or improper fractions in simplest form.

[tex]f = [/tex] [tex]\square[/tex] or [tex]f = [/tex] [tex]\square[/tex]

To solve the equation [tex]$62 = |f + 4|$[/tex], we need to consider the properties of absolute values. An absolute value expression [tex]$|x|$[/tex] can be split into two cases:

1. [tex]$x$[/tex] is already non-negative, so [tex]$|x| = x$[/tex].
2. [tex]$x$[/tex] is negative, so [tex]$|x| = -x$[/tex].

Considering these cases for the equation [tex]$62 = |f + 4|$[/tex], we can write:

Case 1: [tex]$f + 4 = 62$[/tex]
- Solve for [tex]$f$[/tex] by isolating it:
[tex]\[
f + 4 = 62
\][/tex]
[tex]\[
f = 62 - 4
\][/tex]
[tex]\[
f = 58
\][/tex]

Case 2: [tex]$f + 4 = -62$[/tex]
- Solve for [tex]$f$[/tex] by isolating it:
[tex]\[
f + 4 = -62
\][/tex]
[tex]\[
f = -62 - 4
\][/tex]
[tex]\[
f = -66
\][/tex]

Therefore, the solutions for [tex]$f$[/tex] are [tex]$f = 58$[/tex] and [tex]$f = -66$[/tex].