Answer :
To solve the equation [tex]\(4|x+5| = 16\)[/tex], let's go through the steps:
1. Dividing Both Sides by 4:
Start by dividing both sides of the equation by 4 to isolate the absolute value expression.
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Understanding the Absolute Value:
The equation [tex]\( |x+5| = 4 \)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be 4 or -4. This gives us two separate equations to solve:
- [tex]\(x + 5 = 4\)[/tex]
- [tex]\(x + 5 = -4\)[/tex]
3. Solving the First Equation ([tex]\(x + 5 = 4\)[/tex]):
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
4. Solving the Second Equation ([tex]\(x + 5 = -4\)[/tex]):
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
5. Conclusion:
The solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So, the correct answer is option D. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
1. Dividing Both Sides by 4:
Start by dividing both sides of the equation by 4 to isolate the absolute value expression.
[tex]\[
|x+5| = \frac{16}{4} = 4
\][/tex]
2. Understanding the Absolute Value:
The equation [tex]\( |x+5| = 4 \)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be 4 or -4. This gives us two separate equations to solve:
- [tex]\(x + 5 = 4\)[/tex]
- [tex]\(x + 5 = -4\)[/tex]
3. Solving the First Equation ([tex]\(x + 5 = 4\)[/tex]):
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
4. Solving the Second Equation ([tex]\(x + 5 = -4\)[/tex]):
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
5. Conclusion:
The solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
So, the correct answer is option D. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].