High School

Solve for [tex]x[/tex]:

[tex]-4|x+5|=-16[/tex]

A. [tex]x=\frac{21}{4}, x=-\frac{11}{4}[/tex]

B. [tex]x=-1, x=9[/tex]

C. [tex]x=-1, x=-9[/tex]

D. No solution

Answer :

Let's solve the equation [tex]\(-4|x+5| = -16\)[/tex] step by step:

1. Isolate the Absolute Value:
- Divide both sides of the equation by [tex]\(-4\)[/tex] to get [tex]\(|x+5| = 4\)[/tex].

2. Remove the Absolute Value:
- The equation [tex]\(|x+5| = 4\)[/tex] implies two separate equations:
- [tex]\(x + 5 = 4\)[/tex]
- [tex]\(x + 5 = -4\)[/tex]

3. Solve Each Equation Separately:

- First Equation:
- [tex]\(x + 5 = 4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]

- Second Equation:
- [tex]\(x + 5 = -4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]

4. Solution:
- The solutions for the given equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].

So, the correct set of solutions is: [tex]\( x = -1, x = -9 \)[/tex].

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