Complete Guide Linear Inequalities
Linear inequalities compare two linear expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other. On the SAT, you'll often need to graph these on a number line or interpret a given graph.
1. Graph Inequalities
To graph an inequality, find the number on the number line. Use an open circle ( O ) for > (greater than) and < (less than). Use a closed circle ( ● ) for ≥ (greater than or equal to) and ≤ (less than or equal to). Then, shade in the direction that makes the inequality true.
Interactive Grapher
Enter an inequality below to see it graphed on the number line. The view centers on your boundary. This teaching graph accepts finite values from −1,000,000 to 1,000,000 to keep its five-unit tick spacing accurate; decimals are allowed.
2. Write Inequalities from Graphs
To write an inequality from a graph, first identify the key number. Note whether the circle is open or closed. Finally, determine the direction of the shading to choose the correct inequality symbol.
What's the Inequality?
Below is a graph of an inequality. Write the correct inequality in the boxes.
Ready to Practice?
Choose an activity to master linear inequalities.
Key Concepts: Flashcards
Click the card or press Enter or Space to flip it. Use the buttons to review.
Inequalities: Practice Quiz
Sources
For more on inequality symbols, endpoint inclusion and number-line graphs: