Respuesta :
Considering the absolute value inequality [tex]|x + 11| < 17[/tex], the solution is:
- A. x< 6 and x < -28
The absolute value function is defined by:
[tex]|f(x)| = x, x \geq 0[/tex]
[tex]|f(x)| = -x, x < 0[/tex]
- It measures the distance of a point x to the origin.
Hence, the inequality:
[tex]|f(x) < a|[/tex]
Has solution given by:
[tex]-a < f(x) < a[/tex]
In this problem, the inequality is:
[tex]|x + 11| < 17[/tex]
Then:
[tex]-17 < x + 11 < 17[/tex]
[tex]x + 11 > -17[/tex]
[tex]x > -28[/tex]
[tex]x + 11 < 17[/tex]
[tex]x < 6[/tex]
Both conditions are necessary, hence, option a is correct.
To learn more about absolute value, you can take a look at https://brainly.com/question/24514895
