Answer :
To solve the equation [tex]\(4|x+5|=16\)[/tex], follow these steps:
1. Isolate the absolute value expression:
Divide each side of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
[tex]\[
|x+5| = 4
\][/tex]
2. Set up two separate equations:
The absolute value [tex]\( |x+5| = 4 \)[/tex] means that the inside of the absolute value, [tex]\( x+5 \)[/tex], can be either 4 or -4.
- First equation:
[tex]\[
x + 5 = 4
\][/tex]
Subtract 5 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Second equation:
[tex]\[
x + 5 = -4
\][/tex]
Subtract 5 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Write the solutions:
The solutions for the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Thus, the correct answer is:
C. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Isolate the absolute value expression:
Divide each side of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
[tex]\[
|x+5| = 4
\][/tex]
2. Set up two separate equations:
The absolute value [tex]\( |x+5| = 4 \)[/tex] means that the inside of the absolute value, [tex]\( x+5 \)[/tex], can be either 4 or -4.
- First equation:
[tex]\[
x + 5 = 4
\][/tex]
Subtract 5 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Second equation:
[tex]\[
x + 5 = -4
\][/tex]
Subtract 5 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Write the solutions:
The solutions for the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Thus, the correct answer is:
C. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]