To solve the equation [tex]\( |x - 1| = 8 \)[/tex], we need to consider the definition of the absolute value function. The absolute value of a number [tex]\( y \)[/tex], denoted [tex]\( |y| \)[/tex], is the non-negative value of [tex]\( y \)[/tex] without regard to its sign. Therefore, [tex]\( |x - 1| = 8 \)[/tex] translates to two separate linear equations:
1. [tex]\( x - 1 = 8 \)[/tex]
2. [tex]\( x - 1 = -8 \)[/tex]
Let's solve each equation step by step:
1. Solving [tex]\( x - 1 = 8 \)[/tex]:
[tex]\[
x - 1 = 8
\][/tex]
Add 1 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 8 + 1
\][/tex]
[tex]\[
x = 9
\][/tex]
2. Solving [tex]\( x - 1 = -8 \)[/tex]:
[tex]\[
x - 1 = -8
\][/tex]
Add 1 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = -8 + 1
\][/tex]
[tex]\[
x = -7
\][/tex]
So, the solutions to the equation [tex]\( |x - 1| = 8 \)[/tex] are [tex]\( x = 9 \)[/tex] and [tex]\( x = -7 \)[/tex].
Given the multiple choice options, the solution corresponds to option B:
[tex]\[
\text{B. } x = -7, 9
\][/tex]
