Solve the inequality. Graph the solutions.
StartAbsoluteValue x EndAbsoluteValueplus2greater than10

The inequality is:

\[
|x| + 2 > 10
\]

### Step 1: Isolate the absolute value term.

We start by subtracting 2 from both sides of the inequality:

\[
|x| > 10 - 2
\]

\[
|x| > 8
\]

### Step 2: Break the absolute value inequality into two cases.

Since \( |x| > 8 \), the solutions will be when:

\[
x > 8 \quad \text{or} \quad x < -8
\]

### Step 3: Graph the solution.

The solution consists of all values of \( x \) greater than 8 and less than -8. These are two open intervals:

\[
x \in (-\infty, -8) \cup (8, \infty)
\]

On a number line, this would be represented by two rays extending to the left from \( -8 \) and to the right from \( 8 \), with open circles at \( -8 \) and \( 8 \), indicating that these points are not included in the solution.

### Graph Description:

1. A number line with two open circles at \( -8 \) and \( 8 \).
2. Arrows extending left from \( -8 \) and right from \( 8 \), representing all values less than \( -8 \) and greater than \( 8 \).

Would you like me to generate this graph for you?

### Relative Questions:
1. How do absolute value inequalities differ from regular inequalities?
2. What happens when we reverse the inequality symbol (e.g., \( |x| + 2 < 10 \))?
3. How would the solution change if the inequality was \( |x| + 2 \geq 10 \)?
4. Can you solve a similar inequality, such as \( |x - 5| > 7 \)?
5. How do we graph compound inequalities on a number line?

**Tip:** Always isolate the absolute value term first when solving inequalities!

Solve the inequality. Graph the solutions. |x| + 2 > 10

Learn how to solve the absolute value inequality |x| + 2 > 10 with step-by-step instructions. This problem focuses on absolute value inequalities, isolating the absolute value term, and graphing the solution on a number line. Suitable for students in Grades 8-10.

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