Answer :
Sure! Let's solve the equation [tex]\( 4|x+6| = 16 \)[/tex].
First, we need to isolate the absolute value term. We can do this by dividing both sides of the equation by 4:
[tex]\[ 4|x+6| = 16 \][/tex]
[tex]\[ |x+6| = \frac{16}{4} \][/tex]
[tex]\[ |x+6| = 4 \][/tex]
The absolute value equation [tex]\( |x+6| = 4 \)[/tex] means that [tex]\( x+6 \)[/tex] can be either 4 or -4. This gives us two separate equations to solve:
1. [tex]\( x+6 = 4 \)[/tex]
2. [tex]\( x+6 = -4 \)[/tex]
Let's solve each equation separately:
1. For [tex]\( x+6 = 4 \)[/tex]:
[tex]\[ x + 6 = 4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 4 - 6 \][/tex]
[tex]\[ x = -2 \][/tex]
2. For [tex]\( x+6 = -4 \)[/tex]:
[tex]\[ x + 6 = -4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -4 - 6 \][/tex]
[tex]\[ x = -10 \][/tex]
So, the solutions to the equation [tex]\( 4|x+6| = 16 \)[/tex] are [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex].
Thus, the correct answer is:
C. [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex]
First, we need to isolate the absolute value term. We can do this by dividing both sides of the equation by 4:
[tex]\[ 4|x+6| = 16 \][/tex]
[tex]\[ |x+6| = \frac{16}{4} \][/tex]
[tex]\[ |x+6| = 4 \][/tex]
The absolute value equation [tex]\( |x+6| = 4 \)[/tex] means that [tex]\( x+6 \)[/tex] can be either 4 or -4. This gives us two separate equations to solve:
1. [tex]\( x+6 = 4 \)[/tex]
2. [tex]\( x+6 = -4 \)[/tex]
Let's solve each equation separately:
1. For [tex]\( x+6 = 4 \)[/tex]:
[tex]\[ x + 6 = 4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 4 - 6 \][/tex]
[tex]\[ x = -2 \][/tex]
2. For [tex]\( x+6 = -4 \)[/tex]:
[tex]\[ x + 6 = -4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -4 - 6 \][/tex]
[tex]\[ x = -10 \][/tex]
So, the solutions to the equation [tex]\( 4|x+6| = 16 \)[/tex] are [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex].
Thus, the correct answer is:
C. [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex]