Answer :
To solve the equation [tex]\( 4|x+5|=24 \)[/tex], we can follow these steps:
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set up the two possible equations:
Since we have an absolute value, [tex]\( |x+5| = 6 \)[/tex] means there are two scenarios to consider:
- [tex]\( x + 5 = 6 \)[/tex]
- [tex]\( x + 5 = -6 \)[/tex]
3. Solve each equation separately:
- For the first scenario [tex]\( x + 5 = 6 \)[/tex]:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- For the second scenario [tex]\( x + 5 = -6 \)[/tex]:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Write down the solutions:
The solutions to the equation [tex]\( 4|x+5|=24 \)[/tex] are [tex]\( x = 1 \)[/tex] and [tex]\( x = -11 \)[/tex].
Therefore, the correct answer is B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex].
1. Divide both sides by 4:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set up the two possible equations:
Since we have an absolute value, [tex]\( |x+5| = 6 \)[/tex] means there are two scenarios to consider:
- [tex]\( x + 5 = 6 \)[/tex]
- [tex]\( x + 5 = -6 \)[/tex]
3. Solve each equation separately:
- For the first scenario [tex]\( x + 5 = 6 \)[/tex]:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- For the second scenario [tex]\( x + 5 = -6 \)[/tex]:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Write down the solutions:
The solutions to the equation [tex]\( 4|x+5|=24 \)[/tex] are [tex]\( x = 1 \)[/tex] and [tex]\( x = -11 \)[/tex].
Therefore, the correct answer is B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex].