Answered

IDNLearn.com is your go-to resource for finding precise and accurate answers. Our platform offers reliable and detailed answers, ensuring you have the information you need.

Solve the inequality:

[tex]\[ |x + 6| \ \textless \ 9 \][/tex]

A. [tex]\((-15, -3)\)[/tex]

B. [tex]\((-15, 3)\)[/tex]

C. [tex]\((3, -3)\)[/tex]

D. [tex]\((6, -9)\)[/tex]

Sagot :

GinnyAnsweridn
To solve the inequality [tex]\( |x + 6| < 9 \)[/tex], we need to understand how to work with absolute value inequalities. The absolute value expression [tex]\( |x + 6| \)[/tex] represents the distance of the expression [tex]\( x + 6 \)[/tex] from 0 on the number line.

To remove the absolute value, we split the inequality into two cases based on the definition of absolute value. The inequality [tex]\( |x + 6| < 9 \)[/tex] implies:

[tex]\[ -9 < x + 6 < 9 \][/tex]

Now, we will solve this compound inequality step by step.

1. Start with the inequality:

[tex]\[ -9 < x + 6 < 9 \][/tex]

2. Subtract 6 from each part of the inequality to isolate [tex]\( x \)[/tex]:

[tex]\[ -9 - 6 < x + 6 - 6 < 9 - 6 \][/tex]

This simplifies to:

[tex]\[ -15 < x < 3 \][/tex]

So, the solution to the inequality [tex]\( |x + 6| < 9 \)[/tex] is the open interval [tex]\( (-15, 3) \)[/tex].

Therefore, the correct answer is:

[tex]\[ (-15, 3) \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.