Answer :
Sure! Let's solve the given equation step by step.
The equation we have is:
[tex]\[ 4|x+5| = 16 \][/tex]
### Step 1: Isolate the Absolute Value
First, divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
### Step 2: Set Up Two Equations
The absolute value equation [tex]\( |x+5| = 4 \)[/tex] can be broken down into two separate linear equations:
1. [tex]\( x + 5 = 4 \)[/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
### Step 3: Solve Each Equation
#### Solving Equation 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
#### Solving Equation 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
### Step 4: Combine Solutions
The solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{\text{C. } x = -1 \text{ and } x = -9} \][/tex]
The equation we have is:
[tex]\[ 4|x+5| = 16 \][/tex]
### Step 1: Isolate the Absolute Value
First, divide both sides of the equation by 4 to isolate the absolute value expression:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
### Step 2: Set Up Two Equations
The absolute value equation [tex]\( |x+5| = 4 \)[/tex] can be broken down into two separate linear equations:
1. [tex]\( x + 5 = 4 \)[/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
### Step 3: Solve Each Equation
#### Solving Equation 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
#### Solving Equation 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
### Step 4: Combine Solutions
The solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{\text{C. } x = -1 \text{ and } x = -9} \][/tex]