📚 Practice With Worksheets
Practice graphing inequality solutions, solving inequalities, and interpreting inequality situations in context.
▶️ Learn With Videos
Review how to isolate the variable, reverse an inequality when needed, and represent the solution on a number line.
🛠️ How to Use This Tool
Choose Graph Only to graph an inequality that already has \(x\) isolated. Choose Solve & Graph to solve a one-step or two-step inequality mentally or on paper before graphing its solution.
Move the boundary point to the correct whole number or half-unit value. Choose an open point for \(<\) or \(>\), and choose a closed point for \(\le\) or \(\ge\).
Select Less Than to shade left or Greater Than to shade right, then select Check Graph. In Solve & Graph mode, remember to reverse the inequality when multiplying or dividing by a negative number.
🧠 Things to Notice
The sign of the boundary value does not determine the shading direction. The inequality symbol does: less than shades left, while greater than shades right.
An open point excludes the boundary value. A closed point includes it. Compare \(x<4\) with \(x\le4\).
Before graphing an unsolved inequality, isolate \(x\). If you divide or multiply by a negative number, reverse the inequality symbol before choosing the point type and direction.
📘 Vocabulary
Inequality: A mathematical statement that compares values using \(<\), \(>\), \(\le\), or \(\ge\).
Solution Set: All values that make an inequality true.
Boundary Point: The number where the graphed solution begins or ends.
Less Than: The symbol \(<\) means values smaller than the boundary.
Greater Than: The symbol \(>\) means values larger than the boundary.
Less Than or Equal To: The symbol \(\le\) means values smaller than or equal to the boundary.
Greater Than or Equal To: The symbol \(\ge\) means values larger than or equal to the boundary.
Open Point: Shows that the boundary value is not included in the solution set.
Closed Point: Shows that the boundary value is included in the solution set.
Inverse Operation: An operation used to undo another operation and isolate the variable.
At Most: A phrase that usually translates to \(\le\).
At Least: A phrase that usually translates to \(\ge\).
📐 Solving and Graphing Inequalities
Use inverse operations to isolate the variable before graphing. Addition and subtraction do not change the inequality direction.
\(x+5>8 \Rightarrow x>3\)
Multiplying or dividing both sides by a negative number reverses the inequality symbol.
\(-2x<6 \Rightarrow x>-3\)
Use an open point for strict inequalities and a closed point when equality is included.
\(<,\ > \Rightarrow \text{open point} \qquad \le,\ \ge \Rightarrow \text{closed point}\)
🔗 Share This Math Tool
Found this resource helpful? Share it with another teacher or save the link for later.
🚀 Explore More Math Tools
Browse more interactive tools for algebra, graphing, fractions, geometry, probability, statistics, ratios, and number systems.
Explore More Math Tools