Answer :
To solve the equation [tex]\(4|x+5|=28\)[/tex], let's break it down into a series of steps:
1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 28
\][/tex]
Divide both sides by 4:
[tex]\[
|x+5| = 7
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\( |x+5| = 7 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 7 or -7. This gives us two separate cases to solve:
- Case 1:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 2
\][/tex]
- Case 2:
[tex]\[
x + 5 = -7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -12
\][/tex]
3. Check the solutions:
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
4|2 + 5| = 4 \cdot 7 = 28
\][/tex]
This is a valid solution.
- For [tex]\( x = -12 \)[/tex]:
[tex]\[
4|-12 + 5| = 4 |-7| = 4 \cdot 7 = 28
\][/tex]
This is also a valid solution.
Therefore, the solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
The correct answer is:
C. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]
1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 28
\][/tex]
Divide both sides by 4:
[tex]\[
|x+5| = 7
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\( |x+5| = 7 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 7 or -7. This gives us two separate cases to solve:
- Case 1:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 2
\][/tex]
- Case 2:
[tex]\[
x + 5 = -7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -12
\][/tex]
3. Check the solutions:
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
4|2 + 5| = 4 \cdot 7 = 28
\][/tex]
This is a valid solution.
- For [tex]\( x = -12 \)[/tex]:
[tex]\[
4|-12 + 5| = 4 |-7| = 4 \cdot 7 = 28
\][/tex]
This is also a valid solution.
Therefore, the solutions to the equation [tex]\( 4|x+5| = 28 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
The correct answer is:
C. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]