Answer :
To solve the equation [tex]\(4|x+5|=16\)[/tex], we can follow these steps:
1. Simplify the equation:
Divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[
|x+5| = 4
\][/tex]
2. Remove the absolute value:
The expression [tex]\(|x+5| = 4\)[/tex] implies two cases because the absolute value of a number is the distance from zero, meaning it could be positive or negative.
Case 1: [tex]\(x + 5 = 4\)[/tex]
- Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2: [tex]\(x + 5 = -4\)[/tex]
- Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[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].
Thus, the correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Simplify the equation:
Divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[
|x+5| = 4
\][/tex]
2. Remove the absolute value:
The expression [tex]\(|x+5| = 4\)[/tex] implies two cases because the absolute value of a number is the distance from zero, meaning it could be positive or negative.
Case 1: [tex]\(x + 5 = 4\)[/tex]
- Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2: [tex]\(x + 5 = -4\)[/tex]
- Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[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].
Thus, the correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]