Question

Solve and graph the solutions of the equation –|x – 2| + 9 > 6

Answer 1

Solution:

$\boxed{-1$

Graph:

Option c.

Explanation:

In this exercise we have the following inequality:

$-\mid x - 2 \mid + 9 > 6$

Step 1. Subtract 9 from both sides:

$-\mid x - 2 \mid + 9-9 > 6-9 \\ \\ -\mid x - 2 \mid > -3$

Step 2. Multiply by -1 to both sides

$\mid x - 2 \mid < 3 \ \text{The direction of the inequality changes when multiplying by -1}$

Step 3. Apply property

$\mid x \mid$

So:

$\mid x - 2 \mid < 3 \rightarrow -3$

So the correct option is C.