If a greater than 0​, the solution set of the inequality x squared greater than a consists of all numbers x for which x less than minus StartRoot a EndRoot or x greater than StartRoot a EndRoot.
Solve the inequality.
x squared greater than 81

To solve the inequality \( x^2 > 81 \), we can approach it step by step.

### Step 1: Understand the inequality
The inequality \( x^2 > 81 \) asks for the values of \( x \) where the square of \( x \) is greater than 81.

### Step 2: Express the inequality in terms of square roots
We know that \( x^2 = 81 \) has two solutions: \( x = 9 \) and \( x = -9 \). So, the inequality \( x^2 > 81 \) means \( x \) must be either greater than 9 or less than -9.

### Step 3: Write the solution
The solution to the inequality is:
\[
x > 9 \quad \text{or} \quad x < -9
\]

### Step 4: Express the solution set
In interval notation, the solution set is:
\[
(-\infty, -9) \cup (9, \infty)
\]

So, the solution to the inequality \( x^2 > 81 \) consists of all numbers \( x \) such that \( x < -9 \) or \( x > 9 \).

Would you like more details on this solution, or do you have any questions?

Here are some related questions:

1. What is the solution to the inequality \( x^2 < 64 \)?
2. How would you solve the inequality \( x^2 \geq 49 \)?
3. What is the solution set for the inequality \( x^2 \leq 25 \)?
4. How do you solve the inequality \( x^2 > 100 \)?
5. Can you solve \( x^2 \leq 144 \) and express the solution in interval notation?

**Tip:** When solving inequalities involving squares, always consider both the positive and negative square roots!

Learn how to solve the inequality x^2 > 81 with a detailed step-by-step solution. Understand the concept of inequalities involving squares, use interval notation, and explore the solutions where x is greater than 9 or less than -9. Suitable for Grades 7-9 students studying quadratic equations and inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation