High School

Solve [tex]$4|x+5|+8=24$[/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 :

Sure! Let's solve the equation step by step:

We are given the equation:

[tex]\[ 4|x + 5| + 8 = 24 \][/tex]

First, subtract 8 from both sides to isolate the absolute value term:

[tex]\[ 4|x + 5| + 8 - 8 = 24 - 8 \][/tex]
[tex]\[ 4|x + 5| = 16 \][/tex]

Next, divide both sides by 4 to further isolate the absolute value term:

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

Now we need to consider the two cases for the absolute value equation. The absolute value equation [tex]\( |x + 5| = 4 \)[/tex] can be split into two separate equations:

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

[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]

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

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

So, the solutions to the equation are:

[tex]\[ x = -1 \text{ and } x = -9 \][/tex]

Therefore, the correct answer is:

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