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 :

Sure, let's solve the equation [tex]\(4|x+5|=16\)[/tex] step-by-step.

First, we need to isolate the absolute value expression:

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

Divide both sides by 4:

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

The absolute value equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 4 or -4.

So, we have two cases to consider:

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

Solve for [tex]\( x \)[/tex]:

[tex]\[ x + 5 = 4 \][/tex]
[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]
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]

So, the solutions to the equation [tex]\( 4|x+5| = 16 \)[/tex] are:

[tex]\[ x = -1 \][/tex]
[tex]\[ x = -9 \][/tex]

Therefore, the correct answer is:
A. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]

If you have any more questions, feel free to ask!