Answer :
Certainly! Let's solve the equation step-by-step:
We are given the equation:
[tex]\[ 4|x+6| = 16 \][/tex]
Step 1: Divide both sides of the equation by 4 to simplify.
[tex]\[ |x+6| = \frac{16}{4} \][/tex]
[tex]\[ |x+6| = 4 \][/tex]
Step 2: The equation [tex]\(|x+6| = 4\)[/tex] tells us that the expression inside the absolute value, [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]
Step 3: Solve each equation separately.
- Equation 1:
[tex]\[ x + 6 = 4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 4 - 6 \][/tex]
[tex]\[ x = -2 \][/tex]
- Equation 2:
[tex]\[ x + 6 = -4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -4 - 6 \][/tex]
[tex]\[ x = -10 \][/tex]
Step 4: The solutions to the equation are [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].
So, the correct option is D. [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].
We are given the equation:
[tex]\[ 4|x+6| = 16 \][/tex]
Step 1: Divide both sides of the equation by 4 to simplify.
[tex]\[ |x+6| = \frac{16}{4} \][/tex]
[tex]\[ |x+6| = 4 \][/tex]
Step 2: The equation [tex]\(|x+6| = 4\)[/tex] tells us that the expression inside the absolute value, [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]
Step 3: Solve each equation separately.
- Equation 1:
[tex]\[ x + 6 = 4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 4 - 6 \][/tex]
[tex]\[ x = -2 \][/tex]
- Equation 2:
[tex]\[ x + 6 = -4 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -4 - 6 \][/tex]
[tex]\[ x = -10 \][/tex]
Step 4: The solutions to the equation are [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].
So, the correct option is D. [tex]\(x = -2\)[/tex] and [tex]\(x = -10\)[/tex].