High School

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

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

Answer :

To solve the equation [tex]\( 4|x+5| = 16 \)[/tex], we need to follow these steps:

1. Isolate the Absolute Value:
First, divide both sides of the equation by 4 to simplify it:
[tex]\[
|x + 5| = \frac{16}{4} = 4
\][/tex]

2. Consider the Two Cases for the Absolute Value:
When solving an equation with an absolute value, we consider two cases:

- Case 1: The expression inside the absolute value is positive or zero:
[tex]\[
x + 5 = 4
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]

- Case 2: The expression inside the absolute value is negative:
[tex]\[
x + 5 = -4
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]

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

Given these solutions, the correct answer choice is:

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