Answer
The solution is $f=-1$.
Work Step by Step
The given equation is
$\Rightarrow |f-6|=|f+8|$
Write the two related linear equations.
$f-6=f+8$ ...... (1)
$f-6=-(f+8)$ ...... (2)
Solve equation (1).
$\Rightarrow f-6=f+8$
Add $6-f$ to each side.
$\Rightarrow f-6+6-f=f+8+6-f$
Simplify.
$\Rightarrow 0=14$
False statement.
No solution.
Solve equation (2).
$\Rightarrow f-6=-(f+8)$
Clear the parentheses.
$\Rightarrow f-6=-f-8$
Add $f+6$ to each side.
$\Rightarrow f-6+f+6=-f-8+f+6$
Simplify.
$\Rightarrow 2f=-2$
Divide each side by $2$.
$\Rightarrow \frac{2f}{2}=-\frac{2}{2}$
Simplify.
$\Rightarrow f=-1$
Check : $f=-1$
$\Rightarrow |f-6|=|f+8|$
$\Rightarrow |-1-6|=|-1+8|$
$\Rightarrow |-7|=|7|$
$\Rightarrow 7=7$
True.
Hence, the solution is $f=-1$.
