High School

Solve [tex]$4|x+5|=16$[/tex]

A. [tex]$x=1$[/tex] and [tex]$x=-9$[/tex]
B. [tex]$x=-1$[/tex] and [tex]$x=-9$[/tex]
C. [tex]$x=-1$[/tex] and [tex]$x=9$[/tex]
D. [tex]$x=1$[/tex] and [tex]$x=-1$[/tex]

Answer :

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

1. Isolate the absolute value:
Start by dividing both sides of the equation by 4 to simplify it:

[tex]\[
|x+5| = \frac{16}{4}
\][/tex]

[tex]\[
|x+5| = 4
\][/tex]

2. Understand the absolute value:
The equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can be either 4 or -4. This is because the absolute value of a number is its distance from zero on the number line, which is always positive.

3. Set up the two cases:

Case 1: [tex]\(x + 5 = 4\)[/tex]
- Solve for [tex]\(x\)[/tex]:

[tex]\[
x + 5 = 4
\][/tex]

Subtract 5 from both sides:

[tex]\[
x = 4 - 5
\][/tex]

[tex]\[
x = -1
\][/tex]

Case 2: [tex]\(x + 5 = -4\)[/tex]
- Solve for [tex]\(x\)[/tex]:

[tex]\[
x + 5 = -4
\][/tex]

Subtract 5 from both sides:

[tex]\[
x = -4 - 5
\][/tex]

[tex]\[
x = -9
\][/tex]

4. Solutions:
The solutions to the equation [tex]\(4|x+5| = 16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].

From the given options, the correct answer is:

B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].