Answer :
Sure, let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4|x + 5| + 8 = 24 \][/tex]
First, isolate the absolute value term:
[tex]\[ 4|x + 5| = 24 - 8 \][/tex]
[tex]\[ 4|x + 5| = 16 \][/tex]
Next, divide both sides by 4:
[tex]\[ |x + 5| = 4 \][/tex]
Now, we need to solve for [tex]\( x \)[/tex] in the absolute value equation. The absolute value equation [tex]\( |x + 5| = 4 \)[/tex] means that:
[tex]\[ x + 5 = 4 \quad \text{or} \quad x + 5 = -4 \][/tex]
Solve each equation separately:
1. [tex]\( x + 5 = 4 \)[/tex]
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the solutions to the equation [tex]\( 4|x + 5| + 8 = 24 \)[/tex] are:
[tex]\[ x = -1 \quad \text{and} \quad x = -9 \][/tex]
Therefore, the correct answer is:
[tex]\[ x = -9 \, \text{and} \, x = -1 \][/tex]
So, the correct choice from the given options is:
[tex]\[ x = -9 \, \text{and} \, x = -1 \][/tex]
The given equation is:
[tex]\[ 4|x + 5| + 8 = 24 \][/tex]
First, isolate the absolute value term:
[tex]\[ 4|x + 5| = 24 - 8 \][/tex]
[tex]\[ 4|x + 5| = 16 \][/tex]
Next, divide both sides by 4:
[tex]\[ |x + 5| = 4 \][/tex]
Now, we need to solve for [tex]\( x \)[/tex] in the absolute value equation. The absolute value equation [tex]\( |x + 5| = 4 \)[/tex] means that:
[tex]\[ x + 5 = 4 \quad \text{or} \quad x + 5 = -4 \][/tex]
Solve each equation separately:
1. [tex]\( x + 5 = 4 \)[/tex]
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the solutions to the equation [tex]\( 4|x + 5| + 8 = 24 \)[/tex] are:
[tex]\[ x = -1 \quad \text{and} \quad x = -9 \][/tex]
Therefore, the correct answer is:
[tex]\[ x = -9 \, \text{and} \, x = -1 \][/tex]
So, the correct choice from the given options is:
[tex]\[ x = -9 \, \text{and} \, x = -1 \][/tex]