To simplify the inequality \( 2x - 5 \geq 5 - 2x \):

1. First, add \( 2x \) to both sides to eliminate the \( -2x \) on the right:
   \[
   2x + 2x - 5 \geq 5
   \]
   This simplifies to:
   \[
   4x - 5 \geq 5
   \]

2. Next, add 5 to both sides to isolate terms with \( x \) on the left:
   \[
   4x - 5 + 5 \geq 5 + 5
   \]
   Simplifying:
   \[
   4x \geq 10
   \]

3. Finally, divide both sides by 4:
   \[
   x \geq \frac{10}{4}
   \]
   Simplifying further:
   \[
   x \geq 2.5
   \]

Thus, the solution is \( x \geq 2.5 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve inequalities with fractions?
2. What happens if you multiply or divide by a negative number in inequalities?
3. Can inequalities have multiple solutions?
4. How do you graph an inequality on a number line?
5. How can you verify the solution to an inequality?

**Tip:** When multiplying or dividing both sides of an inequality by a negative number, remember to reverse the inequality sign!

This guide explains how to solve the linear inequality 2x - 5 ≥ 5 - 2x step by step. It covers essential algebraic concepts like inequality manipulation, isolating variables, and key properties of inequalities. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation