Answer :
To solve the equation [tex]\( 4|x+5| = 16 \)[/tex], let's follow these steps:
1. Isolate the absolute value:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the definition of absolute value:
An absolute value equation [tex]\( |a| = b \)[/tex] means that [tex]\( a = b \)[/tex] or [tex]\( a = -b \)[/tex]. So we have:
[tex]\[
x + 5 = 4 \quad \text{or} \quad x + 5 = -4
\][/tex]
3. Solve each case separately:
- For [tex]\( x + 5 = 4 \)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For [tex]\( x + 5 = -4 \)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
4. Combine the solutions:
The solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are:
[tex]\[
x = -1 \quad \text{and} \quad x = -9
\][/tex]
So the correct answer is B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
1. Isolate the absolute value:
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Consider the definition of absolute value:
An absolute value equation [tex]\( |a| = b \)[/tex] means that [tex]\( a = b \)[/tex] or [tex]\( a = -b \)[/tex]. So we have:
[tex]\[
x + 5 = 4 \quad \text{or} \quad x + 5 = -4
\][/tex]
3. Solve each case separately:
- For [tex]\( x + 5 = 4 \)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For [tex]\( x + 5 = -4 \)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
4. Combine the solutions:
The solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are:
[tex]\[
x = -1 \quad \text{and} \quad x = -9
\][/tex]
So the correct answer is B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].