Answer :
Sure, let's solve the equation step by step:
We start with the given equation:
[tex]\[ 4|x+5|=16 \][/tex]
1. First, isolate the absolute value term on one side by dividing both sides of the equation by 4:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
2. The absolute value equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value can be equal to 4 or -4. So, we write two separate equations to consider both cases:
[tex]\[ x+5 = 4 \][/tex]
[tex]\[ x+5 = -4 \][/tex]
3. Solve each equation separately:
- For [tex]\( x+5 = 4 \)[/tex]:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\( x+5 = -4 \)[/tex]:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
4. Thus, we have two solutions for the equation:
[tex]\[ x = -1 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the correct answer is:
[tex]\[ D. \, x = -1 \, \text{and} \, x = -9 \][/tex]
We start with the given equation:
[tex]\[ 4|x+5|=16 \][/tex]
1. First, isolate the absolute value term on one side by dividing both sides of the equation by 4:
[tex]\[ |x+5| = \frac{16}{4} \][/tex]
[tex]\[ |x+5| = 4 \][/tex]
2. The absolute value equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value can be equal to 4 or -4. So, we write two separate equations to consider both cases:
[tex]\[ x+5 = 4 \][/tex]
[tex]\[ x+5 = -4 \][/tex]
3. Solve each equation separately:
- For [tex]\( x+5 = 4 \)[/tex]:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- For [tex]\( x+5 = -4 \)[/tex]:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
4. Thus, we have two solutions for the equation:
[tex]\[ x = -1 \][/tex]
[tex]\[ x = -9 \][/tex]
So, the correct answer is:
[tex]\[ D. \, x = -1 \, \text{and} \, x = -9 \][/tex]