Draw Inequalities or Systems With Our Free Grapher

Graph, plot or draw inequalities or systems of inequalities with our free step-by-step algebra inequality grapher.

Inequalities can be tricky enough when you're solving them on paper, but things get really confusing when you need to draw inequalities on a coordinate plane. Which side do you shade? Is the line solid or dashed? And what happens when you have to plot systems of inequalities and figure out where all the shaded regions overlap? If you've ever stared at a blank graph wondering where to even start, you're in the right place.

Why Graphing Inequalities Matters

Graphing isn't just busywork your teacher assigns to fill time. When you draw inequalities, you're creating a visual picture of all the possible solutions at once. Instead of a single answer, you get an entire region of values that work. This becomes really powerful when you're dealing with real-world situations like budgeting (you can spend up to a certain amount), scheduling (you need at least this many hours), or any scenario with limits and constraints. Learning to solve inequalities by graphing helps you see the math, not just calculate it.

Single Inequalities: Getting the Basics Right

Before you can tackle systems, you need to be comfortable graphing a single inequality. The process starts with graphing the boundary line, which is the equation you get when you replace the inequality sign with an equals sign. If your inequality uses < or >, the line is dashed because points on the line aren't included in the solution. If it uses ≤ or ≥, the line is solid because those points are part of the solution.

Next comes shading. You need to figure out which side of the line contains all the points that make the inequality true. A quick way to check is to pick a test point (like the origin, if it's not on the line) and plug it into the inequality. If it works, shade that side. If not, shade the other side. Our free step-by-step algebra inequality grapher does all of this for you and shows you why each decision is made, so you learn the reasoning as you go.

Systems of Inequalities: Where It Gets Interesting

When you plot systems of inequalities, you're graphing two or more inequalities on the same coordinate plane. Each inequality has its own boundary line and shaded region. The solution to the system is where all the shaded regions overlap. This overlapping area represents every point that satisfies all the inequalities at the same time.

Systems of inequalities come up constantly in real applications. Think about problems where you have multiple constraints: you need to buy at least 10 items but spend no more than $50, or you need to work enough hours at two jobs to meet a minimum income while not exceeding a maximum number of hours per week. When you graph these situations, the feasible region (the overlap) shows you all your options at a glance.

Common Mistakes and How to Avoid Them

One of the biggest errors students make is using the wrong type of line. Always double-check whether your inequality is strict (< or >) or inclusive (≤ or ≥) before you draw. Another common mistake is shading the wrong region. If you skip the test point step, it's easy to guess wrong. And when working with systems, make sure you're identifying the overlap correctly, not just shading everything.

Using a tool to draw inequalities lets you check your work instantly. You can see whether your hand-drawn graph matches and understand where you went wrong if it doesn't.

Learn by Seeing Every Step

QuickMath's inequality grapher doesn't just spit out a finished graph. It walks you through each step with explanations: how to identify the boundary line, why it's solid or dashed, how to determine the correct shading, and how to find the solution region for systems. And it's completely free. So whether you're doing homework, prepping for a test, or just trying to finally understand this topic, you can solve inequalities by graphing with confidence and actually learn the process along the way.