evaluate the expression when a = , b = -3, c = -12
|a + b + c| = 22
is 22 the correct answer?
What does a equal?
a = 7
no
|7-3-12}
= |-8|
= 8
you did |7| + |-3| + |-12| , which was not the question
To evaluate the expression |a + b + c| = 22, we substitute the given values of a, b, and c.
Given:
a = ?
b = -3
c = -12
Substituting these values into the expression:
|a + (-3) + (-12)| = 22
Simplifying the expression inside the absolute value:
|a - 3 - 12| = 22
|a - 15| = 22
To find the value of a, we need to isolate the absolute value expression by solving two separate equations:
1. (a - 15) = 22
2. -(a - 15) = 22
Solving equation 1:
a - 15 = 22
a = 22 + 15
a = 37
Solving equation 2:
-(a - 15) = 22
-a + 15 = 22
-a = 22 - 15
-a = 7
a = -7
So, we have two possible values for a: a = 37 and a = -7.
To determine whether 22 is the correct answer, we need to substitute both values of a into the original equation:
For a = 37:
|37 + (-3) + (-12)| = 22
|37 - 3 - 12| = 22
|22| = 22
For a = -7:
|-7 + (-3) + (-12)| = 22
|-7 - 3 - 12| = 22
|-22| = 22
In both cases, the absolute value expression evaluates to 22, so YES, 22 is the correct answer.