Answer :
Let's solve the equation [tex]\(4|x+6| = 16\)[/tex].
1. First, divide both sides of the equation by 4 to simplify it:
[tex]\[
|x+6| = 4
\][/tex]
2. The absolute value equation [tex]\( |x+6| = 4 \)[/tex] means that the expression inside the absolute value can be either 4 or -4. This gives us two separate equations to solve:
a) [tex]\( x+6 = 4 \)[/tex]
b) [tex]\( x+6 = -4 \)[/tex]
3. Solve each equation separately:
a) For [tex]\( x+6 = 4 \)[/tex]:
[tex]\[
x = 4 - 6
\][/tex]
[tex]\[
x = -2
\][/tex]
b) For [tex]\( x+6 = -4 \)[/tex]:
[tex]\[
x = -4 - 6
\][/tex]
[tex]\[
x = -10
\][/tex]
4. Therefore, the solutions to the equation [tex]\(4|x+6| = 16\)[/tex] are [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex].
So, the correct answer is B. [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].
1. First, divide both sides of the equation by 4 to simplify it:
[tex]\[
|x+6| = 4
\][/tex]
2. The absolute value equation [tex]\( |x+6| = 4 \)[/tex] means that the expression inside the absolute value can be either 4 or -4. This gives us two separate equations to solve:
a) [tex]\( x+6 = 4 \)[/tex]
b) [tex]\( x+6 = -4 \)[/tex]
3. Solve each equation separately:
a) For [tex]\( x+6 = 4 \)[/tex]:
[tex]\[
x = 4 - 6
\][/tex]
[tex]\[
x = -2
\][/tex]
b) For [tex]\( x+6 = -4 \)[/tex]:
[tex]\[
x = -4 - 6
\][/tex]
[tex]\[
x = -10
\][/tex]
4. Therefore, the solutions to the equation [tex]\(4|x+6| = 16\)[/tex] are [tex]\( x = -2 \)[/tex] and [tex]\( x = -10 \)[/tex].
So, the correct answer is B. [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].