Solution:
[tex]\boxed{-1<x<5}[/tex]
Graph:
Option c.
Explanation:
In this exercise we have the following inequality:
[tex]-\mid x - 2 \mid + 9 > 6[/tex]
Step 1. Subtract 9 from both sides:
[tex]-\mid x - 2 \mid + 9-9 > 6-9 \\ \\ -\mid x - 2 \mid > -3[/tex]
Step 2. Multiply by -1 to both sides
[tex]\mid x - 2 \mid < 3 \ \text{The direction of the inequality changes when multiplying by -1}[/tex]
Step 3. Apply property
[tex]\mid x \mid <a \rightarrow -a<x<a[/tex]
So:
[tex]\mid x - 2 \mid < 3 \rightarrow -3<x-2<3 \\ \\ Adding \ 2: \\ \\ -3+2<x-2+2<3+2 \\ \\ \boxed{-1<x<5}[/tex]
So the correct option is C.
