To evaluate the expression [tex]\(\frac{|b-c|-a}{6}\)[/tex] using the given values [tex]\( a = 10 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = 6 \)[/tex], follow these detailed steps:
1. Calculate the absolute difference:
[tex]\[
|b - c| = |10 - 6|
\][/tex]
Evaluate the difference:
[tex]\[
10 - 6 = 4
\][/tex]
Take the absolute value (which is just 4 in this case since the result is positive):
[tex]\[
|4| = 4
\][/tex]
2. Subtract [tex]\(a\)[/tex] from the result:
[tex]\[
4 - a = 4 - 10
\][/tex]
Evaluate the subtraction:
[tex]\[
4 - 10 = -6
\][/tex]
3. Divide the result by 6:
[tex]\[
\frac{-6}{6}
\][/tex]
Evaluate the division:
[tex]\[
\frac{-6}{6} = -1
\][/tex]
Thus, the expression [tex]\(\frac{|b-c|-a}{6}\)[/tex] evaluates to [tex]\(-1\)[/tex].
Therefore, the correct answer is:
A) [tex]\(-1\)[/tex]
