Answer :
Let's solve the equation step by step:
The equation we need to solve is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
1. Isolate the Absolute Value:
Subtract 8 from both sides of the equation:
[tex]\[ 4|x+5| = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
2. Divide Both Sides by 4:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
3. Set Up Two Equations:
The absolute value equation [tex]\( |x+5| = 4 \)[/tex] gives us two possible equations, since the expression inside the absolute value can be either positive or negative:
- [tex]\( x+5 = 4 \)[/tex]
- [tex]\( x+5 = -4 \)[/tex]
4. Solve Each Equation:
- For [tex]\( x+5 = 4 \)[/tex]:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\( x+5 = -4 \)[/tex]:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
Therefore, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
The correct answer from the choices is:
B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
The equation we need to solve is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
1. Isolate the Absolute Value:
Subtract 8 from both sides of the equation:
[tex]\[ 4|x+5| = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
2. Divide Both Sides by 4:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
3. Set Up Two Equations:
The absolute value equation [tex]\( |x+5| = 4 \)[/tex] gives us two possible equations, since the expression inside the absolute value can be either positive or negative:
- [tex]\( x+5 = 4 \)[/tex]
- [tex]\( x+5 = -4 \)[/tex]
4. Solve Each Equation:
- For [tex]\( x+5 = 4 \)[/tex]:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\( x+5 = -4 \)[/tex]:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
Therefore, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
The correct answer from the choices is:
B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]