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.
