Answer :
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].
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].
