Answer :
Sure, let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4|x+5| = 24 \][/tex]
Step 1: Divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[ |x+5| = \frac{24}{4} \][/tex]
[tex]\[ |x+5| = 6 \][/tex]
Step 2: Consider the definition of absolute value. The equation [tex]\(|x+5| = 6\)[/tex] implies two scenarios:
1. [tex]\( x + 5 = 6 \)[/tex]
2. [tex]\( x + 5 = -6 \)[/tex]
Step 3: Solve each scenario separately.
Scenario 1:
[tex]\[ x + 5 = 6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 6 - 5 \][/tex]
[tex]\[ x = 1 \][/tex]
Scenario 2:
[tex]\[ x + 5 = -6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -6 - 5 \][/tex]
[tex]\[ x = -11 \][/tex]
Hence, the solutions to the equation [tex]\( 4|x+5| = 24 \)[/tex] are:
[tex]\[ x = 1 \text{ and } x = -11 \][/tex]
So, the correct answer is:
A. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]
The given equation is:
[tex]\[ 4|x+5| = 24 \][/tex]
Step 1: Divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[ |x+5| = \frac{24}{4} \][/tex]
[tex]\[ |x+5| = 6 \][/tex]
Step 2: Consider the definition of absolute value. The equation [tex]\(|x+5| = 6\)[/tex] implies two scenarios:
1. [tex]\( x + 5 = 6 \)[/tex]
2. [tex]\( x + 5 = -6 \)[/tex]
Step 3: Solve each scenario separately.
Scenario 1:
[tex]\[ x + 5 = 6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 6 - 5 \][/tex]
[tex]\[ x = 1 \][/tex]
Scenario 2:
[tex]\[ x + 5 = -6 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -6 - 5 \][/tex]
[tex]\[ x = -11 \][/tex]
Hence, the solutions to the equation [tex]\( 4|x+5| = 24 \)[/tex] are:
[tex]\[ x = 1 \text{ and } x = -11 \][/tex]
So, the correct answer is:
A. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]