Question 5 of 10

Which of the following is (are) the solution(s) to [tex][tex]$|x-1|=8$[/tex][/tex]?

A. [tex][tex]$x=7$[/tex][/tex]
B. [tex][tex]$x=-7, 9$[/tex][/tex]
C. [tex][tex]$x=9$[/tex][/tex]
D. [tex][tex]$x=7, -9$[/tex][/tex]



Answer :

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]