Answer :
Certainly! Let's solve the equation [tex]\(4|x+5|=16\)[/tex] step-by-step.
1. Isolate the absolute value expression:
First, we need to isolate [tex]\(|x+5|\)[/tex] by dividing both sides of the equation by 4:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the two cases for the absolute value:
The equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can be either 4 or -4:
- Case 1: [tex]\(x + 5 = 4\)[/tex]
- Solving for [tex]\(x\)[/tex], we subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: [tex]\(x + 5 = -4\)[/tex]
- Solving for [tex]\(x\)[/tex], we again subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
3. Conclusion:
The solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So, the correct answer is [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex], which corresponds to option B.
1. Isolate the absolute value expression:
First, we need to isolate [tex]\(|x+5|\)[/tex] by dividing both sides of the equation by 4:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the two cases for the absolute value:
The equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can be either 4 or -4:
- Case 1: [tex]\(x + 5 = 4\)[/tex]
- Solving for [tex]\(x\)[/tex], we subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: [tex]\(x + 5 = -4\)[/tex]
- Solving for [tex]\(x\)[/tex], we again subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
3. Conclusion:
The solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So, the correct answer is [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex], which corresponds to option B.