Answer :
To solve the equation [tex]\(4|x+5| = 28\)[/tex], let's go through it step-by-step:
1. Isolate the Absolute Value:
Begin by dividing both sides of the equation by 4 to isolate the absolute value:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Consider the Two Cases for Absolute Value:
Absolute values can have two cases, because the expression inside can be either positive or negative.
- Case 1: [tex]\(x + 5 = 7\)[/tex]
- Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
- Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = -7 - 5 = -12
\][/tex]
3. Identify the Solutions:
The solutions to the equation [tex]\(4|x+5| = 28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Thus, the correct option is:
C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]
1. Isolate the Absolute Value:
Begin by dividing both sides of the equation by 4 to isolate the absolute value:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]
2. Consider the Two Cases for Absolute Value:
Absolute values can have two cases, because the expression inside can be either positive or negative.
- Case 1: [tex]\(x + 5 = 7\)[/tex]
- Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- Case 2: [tex]\(x + 5 = -7\)[/tex]
- Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = -7 - 5 = -12
\][/tex]
3. Identify the Solutions:
The solutions to the equation [tex]\(4|x+5| = 28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].
Thus, the correct option is:
C. [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex]