To solve the problem of finding which expression is equivalent to [tex]\( |-12 + 3| \)[/tex], we need to follow these steps:
1. Compute the value of [tex]\( |-12 + 3| \)[/tex]:
[tex]\[
-12 + 3 = -9
\][/tex]
Taking the absolute value of [tex]\(-9\)[/tex], we get:
[tex]\[
|-9| = 9
\][/tex]
2. Evaluate each of the given expressions:
- For [tex]\(-12 + |3|\)[/tex]:
[tex]\[
-12 + |3| = -12 + 3 = -9
\][/tex]
- For [tex]\(-12 - |3|\)[/tex]:
[tex]\[
-12 - |3| = -12 - 3 = -15
\][/tex]
- For [tex]\(12 - |3|\)[/tex]:
[tex]\[
12 - |3| = 12 - 3 = 9
\][/tex]
- For [tex]\(12 + |3|\)[/tex]:
[tex]\[
12 + |3| = 12 + 3 = 15
\][/tex]
3. Compare each evaluated expression with the computed absolute value [tex]\(9\)[/tex].
From our evaluations:
- [tex]\(-12 + |3| = -9\)[/tex]
- [tex]\(-12 - |3| = -15\)[/tex]
- [tex]\(12 - |3| = 9\)[/tex]
- [tex]\(12 + |3| = 15\)[/tex]
The expression [tex]\(12 - |3|\)[/tex] evaluates to [tex]\(9\)[/tex], which is equivalent to [tex]\(|-12 + 3|\)[/tex].
Therefore, the correct answer is:
[tex]\[ 12 - |3| \][/tex]
Which corresponds to the third option.
