Answer :
Sure! Let's solve the equation [tex]\(4|x+5|=16\)[/tex] step-by-step.
1. Divide Both Sides by 4:
Start by dividing both sides of the equation by 4 to make it simpler:
[tex]\(|x+5| = \frac{16}{4}\)[/tex]
[tex]\(|x+5| = 4\)[/tex]
2. Consider Two Cases for the Absolute Value:
An absolute value equation [tex]\(|x + a| = b\)[/tex] leads to two possible equations:
- Case 1: [tex]\(x + 5 = 4\)[/tex]
- Case 2: [tex]\(x + 5 = -4\)[/tex]
3. Solve Case 1:
- For the equation [tex]\(x + 5 = 4\)[/tex]:
- Subtract 5 from both sides:
[tex]\(x = 4 - 5\)[/tex]
[tex]\(x = -1\)[/tex]
4. Solve Case 2:
- For the equation [tex]\(x + 5 = -4\)[/tex]:
- Subtract 5 from both sides:
[tex]\(x = -4 - 5\)[/tex]
[tex]\(x = -9\)[/tex]
Therefore, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. So, the correct option is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Divide Both Sides by 4:
Start by dividing both sides of the equation by 4 to make it simpler:
[tex]\(|x+5| = \frac{16}{4}\)[/tex]
[tex]\(|x+5| = 4\)[/tex]
2. Consider Two Cases for the Absolute Value:
An absolute value equation [tex]\(|x + a| = b\)[/tex] leads to two possible equations:
- Case 1: [tex]\(x + 5 = 4\)[/tex]
- Case 2: [tex]\(x + 5 = -4\)[/tex]
3. Solve Case 1:
- For the equation [tex]\(x + 5 = 4\)[/tex]:
- Subtract 5 from both sides:
[tex]\(x = 4 - 5\)[/tex]
[tex]\(x = -1\)[/tex]
4. Solve Case 2:
- For the equation [tex]\(x + 5 = -4\)[/tex]:
- Subtract 5 from both sides:
[tex]\(x = -4 - 5\)[/tex]
[tex]\(x = -9\)[/tex]
Therefore, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. So, the correct option is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]