Shocked Your Gina Wilson All Things Algebra Unit 2 Homework 5 Has You Flipping Signs Every Problem! - Carbonext

Understanding the Context

Why Signs Flip in Algebra: The Core Rules

When solving problems involving inequalities or algebraic expressions, a flipped sign usually signals a critical rule: when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality changes. This rule applies to adding or subtracting constants too, but becomes most apparent in inequality manipulation.

Homework 5 Drops the Signal: You Flip Signs Every Problem

In Homework 5 from Gina Wilson’s Algebra Unit 2, students routinely encounter expressions like:

Key Insights

• -2x > 6
  
• x + (−5) < 3
  
• Or any equation where a negative coefficient flips the sign when solved.

The real challenge is reflecting this flip in every step. Missing it means incorrect answers—and frustration. Let’s explore how and why the signs reverse every time.

Step-by-Step Breakdown: Why Sign Flips Happen

1. Inequalities Require Careful Sign Management

Final Thoughts

Unlike equations (where you can add/subtract the same number without flipping), inequalities behave differently:

> When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign.

Example:
Starting with −3x ≤ 12
Divide both sides by −3 — reverse inequality:
x ≥ −4 (not x ≤ −4)

2. Adding or Subtracting Constants

Adding or subtracting a number doesn’t flip signs—your certainty remains intact. For example: