Inequalities work like equations with one critical difference: multiplying or dividing by a negative number flips the inequality sign.

Basic Linear Inequalities

Solve :


Compound Inequalities

Solve :

Subtract 6 from all parts:

Divide by 2:

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Absolute Value Inequalities

means (AND — between)

means OR (OR — outside)

Example:



Systems of Inequalities

The SAT often gives you a graph with a shaded region and asks which point satisfies the system. Just test the point in each inequality.

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Common Mistakes to Avoid

  • Forgetting to flip the sign: This is the number one error. Any time you multiply or divide by a negative, FLIP.
  • Open vs closed circles: and use open circles (not included). and use closed circles (included).
  • Absolute value traps: has NO solution (absolute value is always non-negative).
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SAT Pro Tip

When the SAT shows a system of inequalities on a graph, the shaded region IS the solution. To find which answer choice is in the region, just test each point. Do not try to solve the system algebraically — visual verification is faster.

Practice inequalities with our Linear Inequalities lessons with interactive exercises.