To solve the equation [tex]\(|x + 6| = 8\)[/tex], we need to consider the definition of absolute value. The absolute value of a number is its distance from 0 on the number line, regardless of direction. This means that [tex]\(|x + 6| = 8\)[/tex] has two scenarios:
1. [tex]\(x + 6 = 8\)[/tex]
2. [tex]\(x + 6 = -8\)[/tex]
Let's solve each equation step by step:
### First Scenario: [tex]\(x + 6 = 8\)[/tex]
1. Start with the equation:
[tex]\[ x + 6 = 8 \][/tex]
2. Subtract 6 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x = 8 - 6 \][/tex]
3. Simplify:
[tex]\[ x = 2 \][/tex]
### Second Scenario: [tex]\(x + 6 = -8\)[/tex]
1. Start with the equation:
[tex]\[ x + 6 = -8 \][/tex]
2. Subtract 6 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x = -8 - 6 \][/tex]
3. Simplify:
[tex]\[ x = -14 \][/tex]
So, the solutions to the equation [tex]\(|x + 6| = 8\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -14\)[/tex].
Given the options, the correct answer is:
[tex]\[ \boxed{B. \, x = 2 \, \text{and} \, x = -14} \][/tex]
