To determine which of the given options is equivalent to [tex]\( |-12 + 3| \)[/tex], let's analyze each option step-by-step.
First, we calculate the value of [tex]\( |-12 + 3| \)[/tex]:
[tex]\[ -12 + 3 = -9 \][/tex]
Taking the absolute value:
[tex]\[ |-9| = 9 \][/tex]
So, [tex]\( |-12 + 3| = 9 \)[/tex].
Next, we evaluate each provided option separately.
### Option 1: [tex]\(-|12| + |3|\)[/tex]
[tex]\[ |12| = 12 \][/tex]
[tex]\[ |3| = 3 \][/tex]
[tex]\[ -|12| + |3| = -12 + 3 = -9 \][/tex]
### Option 2: [tex]\(-|12| - |3|\)[/tex]
[tex]\[ |12| = 12 \][/tex]
[tex]\[ |3| = 3 \][/tex]
[tex]\[ -|12| - |3| = -12 - 3 = -15 \][/tex]
### Option 3: [tex]\(|12| - |3|\)[/tex]
[tex]\[ |12| = 12 \][/tex]
[tex]\[ |3| = 3 \][/tex]
[tex]\[ |12| - |3| = 12 - 3 = 9 \][/tex]
### Option 4: [tex]\(|12| + |3|\)[/tex]
[tex]\[ |12| = 12 \][/tex]
[tex]\[ |3| = 3 \][/tex]
[tex]\[ |12| + |3| = 12 + 3 = 15 \][/tex]
We compare the results:
- [tex]\(-|12| + |3| = -9\)[/tex]
- [tex]\(-|12| - |3| = -15\)[/tex]
- [tex]\(|12| - |3| = 9\)[/tex]
- [tex]\(|12| + |3| = 15\)[/tex]
The calculation for [tex]\(|12| - |3| = 9\)[/tex] matches the value of [tex]\( |-12 + 3| = 9 \)[/tex].
Therefore, the equivalent expression to [tex]\( |-12 + 3| \)[/tex] is [tex]\(|12| - |3|\)[/tex].
