Inequalities show up on almost every SAT Math section. The good news? They follow the same rules as equations — with one important twist. Here's everything you need to nail these questions.
What Makes Inequalities Different from Equations?
An inequality uses symbols like , , , or instead of an equals sign. You solve them the same way you solve equations, but there's one critical rule:
When you multiply or divide both sides by a negative number, you must flip the inequality sign.
This is the #1 source of mistakes on inequality questions.
Solving One-Step and Two-Step Inequalities
These are the most common type on the SAT.
Example 1: Solve
Example 2: Solve
Notice the sign flipped in Example 2 because we divided by .
Compound Inequalities
The SAT loves compound inequalities — two inequalities joined together.
Example 3: If , what is the range of ?
Subtract 1 from all three parts:
Divide all three parts by 2:
Inequalities with Variables on Both Sides
Example 4: Solve
SAT-Style Word Problem
Example 5: A phone plan charges a 0.10 per text message. If Marcus wants to spend no more than $45 per month, what is the maximum number of texts he can send?
Set up the inequality:
Marcus can send at most 250 texts.
Practice Problems
Problem 1: Solve
Solution
Remember to flip the sign when dividing by .
Problem 2: If , find the range of .
Solution
Problem 3: A gym charges 15 per month. If Alex has a budget of $150, for how many months can he maintain his membership?
Solution
Alex can afford up to 8 months.
Key Takeaways
- Solve inequalities just like equations — add, subtract, multiply, divide
- Flip the inequality sign when multiplying or dividing by a negative
- For compound inequalities, perform the same operation on all parts
- Always check: does your answer make sense in context?
- On the SAT, watch for answer choices that test whether you remembered to flip the sign
Want more practice? Try NovaMaths — free SAT & ACT math prep with 750+ exercises and an AI tutor.