Answer :
Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
First, we need to isolate the absolute value term. Start by subtracting 8 from both sides:
[tex]\[ 4|x+5| + 8 - 8 = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
Next, divide both sides by 4 to further isolate the absolute value term:
[tex]\[ \frac{4|x+5|}{4} = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
The equation [tex]\( |x+5| = 4 \)[/tex] gives us two cases to consider:
Case 1: [tex]\( x + 5 = 4 \)[/tex]
[tex]\[
x + 5 = 4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2: [tex]\( x + 5 = -4 \)[/tex]
[tex]\[
x + 5 = -4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[ x = -1 \text{ and } x = -9 \][/tex]
Thus, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
The given equation is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
First, we need to isolate the absolute value term. Start by subtracting 8 from both sides:
[tex]\[ 4|x+5| + 8 - 8 = 24 - 8 \][/tex]
[tex]\[ 4|x+5| = 16 \][/tex]
Next, divide both sides by 4 to further isolate the absolute value term:
[tex]\[ \frac{4|x+5|}{4} = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
The equation [tex]\( |x+5| = 4 \)[/tex] gives us two cases to consider:
Case 1: [tex]\( x + 5 = 4 \)[/tex]
[tex]\[
x + 5 = 4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
Case 2: [tex]\( x + 5 = -4 \)[/tex]
[tex]\[
x + 5 = -4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[ x = -1 \text{ and } x = -9 \][/tex]
Thus, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]