Answered

IDNLearn.com makes it easy to find accurate answers to your specific questions. Discover in-depth answers to your questions from our community of experienced professionals.

Select all the correct answers.

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]

Sagot :

GinnyAnsweridn
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]
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.