Answer :
To solve the equation [tex]\(4|x+5| = 16\)[/tex], let's follow these steps:
1. Isolate the absolute value:
Start by dividing both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the two cases for the absolute value:
Since the absolute value of something can either be positive or negative, we set up two separate equations:
- Case 1: [tex]\(x+5 = 4\)[/tex]
- Case 2: [tex]\(x+5 = -4\)[/tex]
3. Solve each case:
- Case 1: Solve the equation [tex]\(x+5 = 4\)[/tex]
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: Solve the equation [tex]\(x+5 = -4\)[/tex]
[tex]\[
x = -4 - 5 = -9
\][/tex]
4. Provide the solutions:
The possible values for [tex]\(x\)[/tex] that satisfy the equation [tex]\(4|x+5| = 16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Isolate the absolute value:
Start by dividing both sides of the equation by 4 to simplify:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the two cases for the absolute value:
Since the absolute value of something can either be positive or negative, we set up two separate equations:
- Case 1: [tex]\(x+5 = 4\)[/tex]
- Case 2: [tex]\(x+5 = -4\)[/tex]
3. Solve each case:
- Case 1: Solve the equation [tex]\(x+5 = 4\)[/tex]
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: Solve the equation [tex]\(x+5 = -4\)[/tex]
[tex]\[
x = -4 - 5 = -9
\][/tex]
4. Provide the solutions:
The possible values for [tex]\(x\)[/tex] that satisfy the equation [tex]\(4|x+5| = 16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]