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Which of the following is equivalent to [tex]$|-12+3|$[/tex]?

A. [tex]-|12|+|3|[/tex]
B. [tex]-|12|-|3|[/tex]
C. [tex]|12|-|3|[/tex]
D. [tex]|12|+|3|[/tex]

Sagot :

GinnyAnsweridn
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].
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