Solve the inequality. Graph the solution.

Question

StartAbsoluteValue x EndAbsoluteValue greater than 9x>9
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

Answer 1

To solve the inequality \( |x| > 9 \), we will break it down into two cases.

1. \( x > 9 \)
2. \( x < -9 \)

Thus, the solution to the inequality \( |x| > 9 \) is:

\[ x > 9 \quad \text{or} \quad x < -9 \]

Solution in Interval Notation

In interval notation, the solution can be written as:

\[ (-\infty, -9) \cup (9, \infty) \]

Graphing the Solution

To graph the solution:

1. Draw an open circle at -9 and shade to the left to represent \( x < -9 \).
2. Draw another open circle at 9 and shade to the right to represent \( x > 9 \).

Graph Representation

\[ \text{--------------o} \quad \text{( -9 )} \quad \text{---------------------} \] \[ \text{-------------------o} \quad \text{( 9 )} \quad \text{----------------------} \]

Final Answer

The solution to the inequality \( |x| > 9 \) is \( x > 9 \) or \( x < -9 \), and the intervals are \( (-\infty, -9) \cup (9, \infty) \).