Question

evaluate each expression if $m = -5$ and $n = 7$.
$|m + n| = $ select choice
$|-m + n| = $ select choice
$-|m + (-n)| = $ select choice
$-|-m| + n = $ select choice
-2
12
2

Explanation:

Step1: Substitute $m=-5,n=7$

$|(-5) + 7| = |2|$

Step2: Compute absolute value

$|2| = 2$

Step1: Substitute $m=-5,n=7$

$|-(-5) + 7| = |5 + 7| = |12|$

Step2: Compute absolute value

$|12| = 12$

Step1: Substitute $m=-5,n=7$

$-|(-5) + (-7)| = |-12|$

Step2: Compute absolute value, apply sign

$-|-12| = -12$

Step1: Substitute $m=-5,n=7$

$-|-(-5)| + 7 = -|5| + 7$

Step2: Compute absolute value, sum values

$-5 + 7 = 2$

Answer:

1. $|m + n| = 2$
2. $|-m + n| = 12$
3. $-|m + (-n)| = -12$
4. $-|-m| + n = 2$