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Question 2 of 10

Which of the following is the solution to [tex]|x+11|\ \textless \ 17[/tex]?

A. [tex]x\ \textless \ 6[/tex] and [tex]x\ \textgreater \ -28[/tex]
B. [tex]x\ \textless \ 6[/tex] and [tex]x\ \textless \ -28[/tex]
C. [tex]x\ \textless \ 6[/tex]
D. [tex]x\ \textless \ 6[/tex] or [tex]x\ \textgreater \ -28[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's solve the inequality [tex]\( |x + 11| < 17 \)[/tex].

The absolute value inequality [tex]\( |x + 11| < 17 \)[/tex] can be broken down into two separate inequalities:

1. [tex]\( x + 11 < 17 \)[/tex]
2. [tex]\( x + 11 > -17 \)[/tex]

Next, we'll solve these inequalities one at a time.

First inequality:
[tex]\[ x + 11 < 17 \][/tex]
To isolate [tex]\( x \)[/tex], we subtract 11 from both sides:
[tex]\[ x < 17 - 11 \][/tex]
[tex]\[ x < 6 \][/tex]

Second inequality:
[tex]\[ x + 11 > -17 \][/tex]
Again, to isolate [tex]\( x \)[/tex], we subtract 11 from both sides:
[tex]\[ x > -17 - 11 \][/tex]
[tex]\[ x > -28 \][/tex]

Combining the results from both inequalities, we get:
[tex]\[ x < 6 \][/tex]
[tex]\[ x > -28 \][/tex]

Therefore, the solution to the inequality [tex]\( |x + 11| < 17 \)[/tex] is:
[tex]\[ -28 < x < 6 \][/tex]

In other words, the correct answer is [tex]\( x < 6 \)[/tex] and [tex]\( x > -28 \)[/tex], which corresponds to option A.

Option A: [tex]\( x < 6 \)[/tex] and [tex]\( x > -28 \)[/tex].

So, the answer to the question is option A.
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