Answer :
To solve the equation [tex]\(4|x+5|=16\)[/tex], we need to isolate the absolute value expression first.
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
Simplifying gives:
[tex]\[
|x+5| = 4
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\( |x+5| = 4 \)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be equal to 4 or -4. This gives us two separate equations to solve:
- Case 1: [tex]\( x+5 = 4 \)[/tex]
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Case 2: [tex]\( x+5 = -4 \)[/tex]
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is C. [tex]\(x=-1\)[/tex] and [tex]\(x=-9\)[/tex].
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
Simplifying gives:
[tex]\[
|x+5| = 4
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\( |x+5| = 4 \)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be equal to 4 or -4. This gives us two separate equations to solve:
- Case 1: [tex]\( x+5 = 4 \)[/tex]
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Case 2: [tex]\( x+5 = -4 \)[/tex]
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is C. [tex]\(x=-1\)[/tex] and [tex]\(x=-9\)[/tex].