To simplify the given expression [tex]\(|x + 7|\)[/tex] for [tex]\(x \geq -7\)[/tex], you need to understand the properties of absolute value functions.
The absolute value of a number, denoted by [tex]\(|a|\)[/tex], is defined as the non-negative value of [tex]\(a\)[/tex]. This means:
- If [tex]\(a\)[/tex] is positive or zero, [tex]\(|a| = a\)[/tex]
- If [tex]\(a\)[/tex] is negative, [tex]\(|a| = -a\)[/tex]
For this particular problem, we have [tex]\(|x + 7|\)[/tex]. The task is to simplify this expression given that [tex]\(x \geq -7\)[/tex].
1. When [tex]\(x \geq -7\)[/tex], the expression inside the absolute value, [tex]\(x + 7\)[/tex], will either be zero or positive. Because of this, the absolute value function will not change the expression:
[tex]\[
|x + 7| = x + 7
\][/tex]
Therefore, the simplified form of [tex]\(|x + 7|\)[/tex] for [tex]\(x \geq -7\)[/tex] is [tex]\(x + 7\)[/tex].
So the correct answer is:
a. [tex]\(x + 7\)[/tex]
