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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 :

GinnyAnswer
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]
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