Answer :
To solve the equation [tex]\(4|x+5| = 16\)[/tex], follow these steps:
1. Isolate the Absolute Value:
Divide both sides of the equation by 4 to simplify the expression. This gives us:
[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 be either 4 or -4. This results in two separate equations:
- [tex]\(x + 5 = 4\)[/tex]
- [tex]\(x + 5 = -4\)[/tex]
3. Solve Each Equation:
- For the first equation [tex]\(x + 5 = 4\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For the second equation [tex]\(x + 5 = -4\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
Thus, the solutions to the equation [tex]\(4|x+5| = 16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct choice is B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
1. Isolate the Absolute Value:
Divide both sides of the equation by 4 to simplify the expression. This gives us:
[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 be either 4 or -4. This results in two separate equations:
- [tex]\(x + 5 = 4\)[/tex]
- [tex]\(x + 5 = -4\)[/tex]
3. Solve Each Equation:
- For the first equation [tex]\(x + 5 = 4\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For the second equation [tex]\(x + 5 = -4\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
Thus, the solutions to the equation [tex]\(4|x+5| = 16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct choice is B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].