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!
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!