Solve the absolute inequality: |2x+2|≥10
	
 x≤−6 or x≥4
	
−6≤x≤4
	
 −6≥x≥−4
	
x≤−4 or x≥6
 

The absolute inequality given is:

\[
|2x + 2| \geq 10
\]

To solve this, let's break it down:

1. The definition of absolute value inequality states that:

   \[
   |A| \geq B \implies A \leq -B \text{ or } A \geq B
   \]

   Applying this to our problem:

   \[
   2x + 2 \leq -10 \quad \text{or} \quad 2x + 2 \geq 10
   \]

2. **Solving the first inequality** \( 2x + 2 \leq -10 \):

   \[
   2x \leq -12
   \]
   \[
   x \leq -6
   \]

3. **Solving the second inequality** \( 2x + 2 \geq 10 \):

   \[
   2x \geq 8
   \]
   \[
   x \geq 4
   \]

Thus, the solution to the inequality is:

\[
x \leq -6 \quad \text{or} \quad x \geq 4
\]

This matches option **1: \( x \leq -6 \) or \( x \geq 4 \)**.

Would you like further details or explanations on any step?

Here are 5 related questions:
1. How do you solve absolute value equations?
2. What is the difference between solving \( |A| \geq B \) and \( |A| \leq B \)?
3. Can you graph the solution of this inequality?
4. What happens if the inequality sign was \( > \) instead of \( \geq \)?
5. How do you solve compound inequalities?

**Tip**: Always isolate the absolute value before applying the rules to split the inequality into two cases.

Solve the absolute inequality: |2x+2|≥10

This page explains how to solve the absolute inequality |2x+2| ≥ 10 using algebraic methods. Understand key concepts like absolute value, inequalities, and the absolute value inequality theorem. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation