Answer :
To solve the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex], follow these steps:
1. Isolate the absolute value expression:
- Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide to simplify:
- Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. Set up the two possible equations:
- Absolute value equations have two scenarios to consider:
- [tex]\( x + 5 = 4 \)[/tex]
- [tex]\( x + 5 = -4 \)[/tex]
4. Solve each equation:
- First equation:
[tex]\[
x + 5 = 4
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Second equation:
[tex]\[
x + 5 = -4
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
Therefore, the solutions to the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]. The correct option is C: [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
1. Isolate the absolute value expression:
- Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide to simplify:
- Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. Set up the two possible equations:
- Absolute value equations have two scenarios to consider:
- [tex]\( x + 5 = 4 \)[/tex]
- [tex]\( x + 5 = -4 \)[/tex]
4. Solve each equation:
- First equation:
[tex]\[
x + 5 = 4
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Second equation:
[tex]\[
x + 5 = -4
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
Therefore, the solutions to the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]. The correct option is C: [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].