Answer :
To solve the equation [tex]\( |f - 8| = 54 \)[/tex], we need to understand what the absolute value equation means. The expression [tex]\( |f - 8| = 54 \)[/tex] tells us that the distance between [tex]\( f \)[/tex] and 8 on a number line is 54 units. This can happen in two scenarios:
1. Case 1: [tex]\( f - 8 = 54 \)[/tex]
To solve this, add 8 to both sides of the equation:
[tex]\[
f - 8 = 54
\][/tex]
[tex]\[
f = 54 + 8
\][/tex]
[tex]\[
f = 62
\][/tex]
2. Case 2: [tex]\( f - 8 = -54 \)[/tex]
Similarly, add 8 to both sides for this case:
[tex]\[
f - 8 = -54
\][/tex]
[tex]\[
f = -54 + 8
\][/tex]
[tex]\[
f = -46
\][/tex]
Therefore, the solutions for the equation [tex]\( |f - 8| = 54 \)[/tex] are [tex]\( f = 62 \)[/tex] and [tex]\( f = -46 \)[/tex].
1. Case 1: [tex]\( f - 8 = 54 \)[/tex]
To solve this, add 8 to both sides of the equation:
[tex]\[
f - 8 = 54
\][/tex]
[tex]\[
f = 54 + 8
\][/tex]
[tex]\[
f = 62
\][/tex]
2. Case 2: [tex]\( f - 8 = -54 \)[/tex]
Similarly, add 8 to both sides for this case:
[tex]\[
f - 8 = -54
\][/tex]
[tex]\[
f = -54 + 8
\][/tex]
[tex]\[
f = -46
\][/tex]
Therefore, the solutions for the equation [tex]\( |f - 8| = 54 \)[/tex] are [tex]\( f = 62 \)[/tex] and [tex]\( f = -46 \)[/tex].
