Answer :
Sure! Let's solve the equation step by step:
We start with the given equation:
[tex]\[ 4|x + 5| = 16 \][/tex]
1. Divide both sides by 4:
[tex]\[ |x + 5| = 4 \][/tex]
2. Solve the absolute value equation:
[tex]\[ |x + 5| = 4 \][/tex]
The absolute value equation [tex]\(|A| = B\)[/tex] can be split into two separate equations: [tex]\(A = B\)[/tex] and [tex]\(A = -B\)[/tex]. Applying this to our equation:
[tex]\[ x + 5 = 4 \quad \text{or} \quad x + 5 = -4 \][/tex]
3. Solve each equation separately:
- For [tex]\(x + 5 = 4\)[/tex]:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\(x + 5 = -4\)[/tex]:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
4. Combine the solutions:
The solutions to the equation are:
[tex]\[ x = -1 \quad \text{and} \quad x = -9 \][/tex]
So, the correct answer is:
[tex]\[ C. \, x = -1 \, \text{and} \, x = -9 \][/tex]
We start with the given equation:
[tex]\[ 4|x + 5| = 16 \][/tex]
1. Divide both sides by 4:
[tex]\[ |x + 5| = 4 \][/tex]
2. Solve the absolute value equation:
[tex]\[ |x + 5| = 4 \][/tex]
The absolute value equation [tex]\(|A| = B\)[/tex] can be split into two separate equations: [tex]\(A = B\)[/tex] and [tex]\(A = -B\)[/tex]. Applying this to our equation:
[tex]\[ x + 5 = 4 \quad \text{or} \quad x + 5 = -4 \][/tex]
3. Solve each equation separately:
- For [tex]\(x + 5 = 4\)[/tex]:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\(x + 5 = -4\)[/tex]:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
4. Combine the solutions:
The solutions to the equation are:
[tex]\[ x = -1 \quad \text{and} \quad x = -9 \][/tex]
So, the correct answer is:
[tex]\[ C. \, x = -1 \, \text{and} \, x = -9 \][/tex]