Answer :
To solve the equation [tex]\(4|x+5|=28\)[/tex], we begin by isolating the absolute value expression.
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{28}{4}
\][/tex]
[tex]\[
|x+5| = 7
\][/tex]
2. Split the absolute value equation into two separate cases. This is because the absolute value of a number, [tex]\(a\)[/tex], can be both [tex]\(a\)[/tex] and [tex]\(-a\)[/tex].
- Case 1:
[tex]\[
x+5 = 7
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- Case 2:
[tex]\[
x+5 = -7
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
3. The solutions for [tex]\(x\)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
So, the correct answer is C. [tex]\(x=-12\)[/tex] and [tex]\(x=2\)[/tex].
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{28}{4}
\][/tex]
[tex]\[
|x+5| = 7
\][/tex]
2. Split the absolute value equation into two separate cases. This is because the absolute value of a number, [tex]\(a\)[/tex], can be both [tex]\(a\)[/tex] and [tex]\(-a\)[/tex].
- Case 1:
[tex]\[
x+5 = 7
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- Case 2:
[tex]\[
x+5 = -7
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -7 - 5
\][/tex]
[tex]\[
x = -12
\][/tex]
3. The solutions for [tex]\(x\)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -12 \)[/tex].
So, the correct answer is C. [tex]\(x=-12\)[/tex] and [tex]\(x=2\)[/tex].