Answer :
Sure, let's solve the equation step-by-step!
The given equation is:
[tex]\[ 4|x+5| = 24 \][/tex]
First, we need to isolate the absolute value expression by dividing both sides of the equation by 4:
[tex]\[ |x+5| = \frac{24}{4} \][/tex]
[tex]\[ |x+5| = 6 \][/tex]
The absolute value equation [tex]\( |x+5| = 6 \)[/tex] can be split into two separate equations:
1. [tex]\( x + 5 = 6 \)[/tex]
2. [tex]\( x + 5 = -6 \)[/tex]
Now, let's solve each equation separately.
1. For [tex]\( x + 5 = 6 \)[/tex]:
[tex]\[ x + 5 = 6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 6 - 5 \][/tex]
[tex]\[ x = 1 \][/tex]
2. For [tex]\( x + 5 = -6 \)[/tex]:
[tex]\[ x + 5 = -6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -6 - 5 \][/tex]
[tex]\[ x = -11 \][/tex]
So, the solutions to the equation [tex]\( 4|x+5| = 24 \)[/tex] are:
[tex]\[ x = 1 \, \text{and} \, x = -11 \][/tex]
Based on the given options:
A. [tex]\( x = 11 \)[/tex] and [tex]\( x = -1 \)[/tex]
B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]
C. [tex]\( x = -11 \)[/tex] and [tex]\( x = -1 \)[/tex]
D. [tex]\( x = 11 \)[/tex] and [tex]\( x = -11 \)[/tex]
The correct answer is:
B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]
The given equation is:
[tex]\[ 4|x+5| = 24 \][/tex]
First, we need to isolate the absolute value expression by dividing both sides of the equation by 4:
[tex]\[ |x+5| = \frac{24}{4} \][/tex]
[tex]\[ |x+5| = 6 \][/tex]
The absolute value equation [tex]\( |x+5| = 6 \)[/tex] can be split into two separate equations:
1. [tex]\( x + 5 = 6 \)[/tex]
2. [tex]\( x + 5 = -6 \)[/tex]
Now, let's solve each equation separately.
1. For [tex]\( x + 5 = 6 \)[/tex]:
[tex]\[ x + 5 = 6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 6 - 5 \][/tex]
[tex]\[ x = 1 \][/tex]
2. For [tex]\( x + 5 = -6 \)[/tex]:
[tex]\[ x + 5 = -6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -6 - 5 \][/tex]
[tex]\[ x = -11 \][/tex]
So, the solutions to the equation [tex]\( 4|x+5| = 24 \)[/tex] are:
[tex]\[ x = 1 \, \text{and} \, x = -11 \][/tex]
Based on the given options:
A. [tex]\( x = 11 \)[/tex] and [tex]\( x = -1 \)[/tex]
B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]
C. [tex]\( x = -11 \)[/tex] and [tex]\( x = -1 \)[/tex]
D. [tex]\( x = 11 \)[/tex] and [tex]\( x = -11 \)[/tex]
The correct answer is:
B. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]