Answer :
To solve the equation [tex]\(|f+9|=81\)[/tex] for [tex]\(f\)[/tex], we need to consider the property of absolute value, which states that [tex]\(|a| = b\)[/tex] implies two possible cases: [tex]\(a = b\)[/tex] or [tex]\(a = -b\)[/tex].
Here's how we apply this to the equation [tex]\(|f+9|=81\)[/tex]:
1. Case 1: [tex]\(f + 9 = 81\)[/tex]
- Subtract 9 from both sides to solve for [tex]\(f\)[/tex]:
[tex]\[
f = 81 - 9
\][/tex]
- Calculate:
[tex]\[
f = 72
\][/tex]
2. Case 2: [tex]\(f + 9 = -81\)[/tex]
- Subtract 9 from both sides to solve for [tex]\(f\)[/tex]:
[tex]\[
f = -81 - 9
\][/tex]
- Calculate:
[tex]\[
f = -90
\][/tex]
Therefore, the solutions for the equation [tex]\(|f+9|=81\)[/tex] are [tex]\(f = 72\)[/tex] and [tex]\(f = -90\)[/tex].
Here's how we apply this to the equation [tex]\(|f+9|=81\)[/tex]:
1. Case 1: [tex]\(f + 9 = 81\)[/tex]
- Subtract 9 from both sides to solve for [tex]\(f\)[/tex]:
[tex]\[
f = 81 - 9
\][/tex]
- Calculate:
[tex]\[
f = 72
\][/tex]
2. Case 2: [tex]\(f + 9 = -81\)[/tex]
- Subtract 9 from both sides to solve for [tex]\(f\)[/tex]:
[tex]\[
f = -81 - 9
\][/tex]
- Calculate:
[tex]\[
f = -90
\][/tex]
Therefore, the solutions for the equation [tex]\(|f+9|=81\)[/tex] are [tex]\(f = 72\)[/tex] and [tex]\(f = -90\)[/tex].
