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Solve the equation [tex]|f-8|=54[/tex] for [tex]f[/tex].

A. [tex]f=62[/tex] and [tex]f=-46[/tex]
B. [tex]f=-64[/tex] and [tex]f=48[/tex]
C. [tex]f=448[/tex] and [tex]f=-448[/tex]
D. [tex]f=7[/tex] and [tex]f=-7[/tex]

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].

Thanks for taking the time to read Solve the equation tex f 8 54 tex for tex f tex A tex f 62 tex and tex f 46 tex B tex f. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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