Rational Inequalities Khan Academy- Algebra Tutorial

What Are Rational Inequalities?

Rational inequalities are fractions where the variable appears in the denominator. You need to find which values make the inequality true.

The standard form looks like this:

R(x)/Q(x) > 0 (or <, ≥, ≤)

Your job is to find the domain restrictions first, then determine where the expression is positive or negative.

This topic sits in Algebra 2 territory. Khan Academy covers it, but the platform's approach has limits you should know about.

Khan Academy's Coverage of Rational Inequalities

Khan Academy offers a dedicated section on rational functions and inequalities. Here's what you'll actually find:

• Video lessons explaining the concept step by step
• Interactive practice problems with instant feedback
• A progression from basic to advanced difficulty
• Mastery points and badges to track progress

The videos are decent for visual learners. Sal Khan walks through examples on a digital whiteboard, which helps if you missed class.

But here's the problem: the explanations can feel surface-level. You get the "how" without enough "why."

The Real Steps for Solving Rational Inequalities

Before you dive into Khan Academy, internalize this process:

Step 1: Set the denominator to zero

This tells you where the expression is undefined. These values are automatically excluded from your solution.

Step 2: Rewrite as an equation

Replace the inequality sign with an equals sign. Solve for the numerator. These are your critical points.

Step 3: Plot on a number line

Mark all critical points: zeros from the numerator and holes from the denominator. These divide your number line into intervals.

Step 4: Test each interval

Pick a test value from each interval. Plug it into the original inequality. Check if the result is true or false.

Step 5: Check your endpoints

Open or closed circles depend on whether the inequality is strict (<, >) or inclusive (≤, ≥). Never include points where the denominator equals zero.

Getting Started on Khan Academy

Here's how to actually use the platform effectively:

1. Search directly — type "rational inequalities" in the search bar
2. Start with the video — watch once at normal speed, then again at 1.5x if you already know the basics
3. Attempt the practice — don't just watch. Khan Academy's strength is the immediate feedback on problems
4. Use the hints sparingly — they're helpful but don't lean on them
5. Track your mastery — aim for 80%+ accuracy before moving on

The platform works best when you're actively solving, not passively watching.

Common Mistakes Students Make

• Forgetting domain restrictions — always identify where the denominator equals zero first
• Multiplying both sides by the denominator — this is dangerous because you don't know if the denominator is positive or negative
• Graphing errors — critical points must be marked correctly (open vs. closed circles)
• Skipping the sign chart — some students try to solve these without visualizing intervals

Khan Academy vs. Other Resources

Here's a quick comparison if you're deciding where to spend your study time:

Khan Academy is fine as a starting point. But if a concept isn't clicking after two sessions, pivot to Paul's Notes or a textbook. Different resources click for different people.

When to Move Beyond Khan Academy

You should look elsewhere if:

• You've completed 20+ problems and still feel uncertain
• The "Hints" button is your first instinct, not your last resort
• You're preparing for an exam and need faster progress
• The platform's pacing feels too slow or too fast

Rational inequalities require pattern recognition. You build that through volume, not through watching the same type of problem solved repeatedly.

Quick Reference: Signs in Rational Inequalities

Keep this mental model:

• Fraction is positive when numerator and denominator have the same sign (both positive or both negative)
• Fraction is negative when numerator and denominator have opposite signs
• Fraction equals zero only when the numerator is zero (and denominator isn't)

This is the logic that drives every sign chart. Master it and the process becomes automatic.

Final Take

Khan Academy works for rational inequalities if you use it correctly. Watch once, practice heavily, and bail if it's not working. Your time is better spent solving 50 problems with partial understanding than watching 10 videos with full understanding.

The skill comes from doing. Get started.