Answer :
To solve the equation [tex]\(4|x+5|=16\)[/tex]:
1. First, isolate the absolute value by dividing both sides of the equation by 4:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. The equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\(x + 5\)[/tex] can be either 4 or -4. We need to consider both cases separately:
Case 1:
[tex]\[
x + 5 = 4
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2:
[tex]\[
x + 5 = -4
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Therefore, the solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
So, the correct answer is:
C. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
1. First, isolate the absolute value by dividing both sides of the equation by 4:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. The equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\(x + 5\)[/tex] can be either 4 or -4. We need to consider both cases separately:
Case 1:
[tex]\[
x + 5 = 4
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2:
[tex]\[
x + 5 = -4
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Therefore, the solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
So, the correct answer is:
C. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].