Answer :
Sure! Let's solve the equation step-by-step.
We have the equation:
[tex]\[ 4|x+5| = 16 \][/tex]
Step 1: Divide both sides of the equation by 4 to isolate the absolute value.
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
Step 2: The absolute value equation [tex]\(|x+5| = 4\)[/tex] can be split into two separate equations:
1. [tex]\( x + 5 = 4 \)[/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
Step 3: Solve each equation separately:
Case 1:
[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]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are:
[tex]\[ x = -1 \text{ and } x = -9 \][/tex]
Therefore, the correct answer is:
C. [tex]\( x = -1 \text{ and } x = -9 \)[/tex]
We have the equation:
[tex]\[ 4|x+5| = 16 \][/tex]
Step 1: Divide both sides of the equation by 4 to isolate the absolute value.
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
Step 2: The absolute value equation [tex]\(|x+5| = 4\)[/tex] can be split into two separate equations:
1. [tex]\( x + 5 = 4 \)[/tex]
2. [tex]\( x + 5 = -4 \)[/tex]
Step 3: Solve each equation separately:
Case 1:
[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]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are:
[tex]\[ x = -1 \text{ and } x = -9 \][/tex]
Therefore, the correct answer is:
C. [tex]\( x = -1 \text{ and } x = -9 \)[/tex]