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Which four inequalities can be used to find the solution to this absolute value inequality?

[tex]\[ 3 \leq |x+2| \leq 6 \][/tex]

A. [tex]\( x+2 \leq -3 \)[/tex]

B. [tex]\( x+2 \leq 6 \)[/tex]

C. [tex]\( x+2 \geq 3 \)[/tex]

D. [tex]\( |x| \leq 4 \)[/tex]

E. [tex]\( |x+2| \geq -6 \)[/tex]

F. [tex]\( x+2 \geq -6 \)[/tex]

G. [tex]\( |x| \geq 1 \)[/tex]

H. [tex]\( |x+2| \leq -3 \)[/tex]



Answer :

GinnyAnswer
To solve the compound absolute value inequality [tex]\( 3 \leq |x+2| \leq 6 \)[/tex], it is essential to consider the properties and implications of absolute value.

The absolute value inequality [tex]\( |x+2| \leq 6 \)[/tex] can be separated into:
1. [tex]\( x+2 \leq 6 \)[/tex]
2. [tex]\( x+2 \geq -6 \)[/tex]

The absolute value inequality [tex]\( |x+2| \geq 3 \)[/tex] can be separated into:
1. [tex]\( x+2 \leq -3 \)[/tex]
2. [tex]\( x+2 \geq 3 \)[/tex]

So, the inequalities that can be used to determine the solution to the given absolute value inequality are:
- [tex]\( x+2 \leq 6 \)[/tex]
- [tex]\( x+2 \geq -6 \)[/tex]
- [tex]\( x+2 \leq -3 \)[/tex]
- [tex]\( x+2 \geq 3 \)[/tex]

Hence, the correct answers are:
- [tex]\( x+2 \leq 6 \)[/tex]
- [tex]\( x+2 \geq -6 \)[/tex]
- [tex]\( x+2 \leq -3 \)[/tex]
- [tex]\( x+2 \geq 3 \)[/tex]

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