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SAT Math skill page

SAT Inequalities Practice

Turn inequality words like at least, at most, greater than, and no more than into clean SAT Math setups.

Practice inequalities in Dolphin SATPractice questions
10-16 min practice time3 questions on pageHeart of Algebra
Practice time10-16 min
Question bank3 questions
Best forHeart of Algebra

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If x + 4 > 10, which inequality is equivalent?
  1. x > 6
  2. x < 6
  3. x > 14
  4. x < 14
Show answer and solution
Correct answerA. x > 6

Solution walkthrough

  1. Subtract 4 from both sides to get x > 6.
Question 2 of 3Medium
Which inequality represents "a number n is at least 12"?
  1. n > 12
  2. n >= 12
  3. n < 12
  4. n <= 12
Show answer and solution
Correct answerB. n >= 12

Solution walkthrough

  1. "At least" includes 12, so the correct symbol is greater than or equal to.
Question 3 of 3Hard
A club can spend no more than $180. If each ticket costs $12, which inequality gives the number t of tickets the club can buy?
  1. 12t < 180
  2. 12t <= 180
  3. t + 12 <= 180
  4. 180t <= 12
Show answer and solution
Correct answerB. 12t <= 180

Solution walkthrough

  1. No more than means less than or equal to.
  2. The total cost is 12t, so 12t <= 180.

Avoid these traps

Common mistakes on this skill

Forgetting to reverse the inequality

Multiplying or dividing both sides by a negative number reverses the inequality symbol.

Ignoring whether the endpoint is included

A strict inequality excludes the boundary value, while <= or >= includes it.

Study plan

How to practice this skill in Dolphin

  1. Solve the inequality while recording any step that uses a negative multiplier or divisor.
  2. Test one value from the proposed solution region in the original inequality.
  3. Match the symbol to the correct endpoint and shading on a graph.
Practice inequalities in Dolphin SAT

Related practice

Build the surrounding skills

SAT Linear Equations PracticeSAT Systems of Equations PracticeSAT Systems of Inequalities PracticeSAT Math skill hub

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FAQ

Questions about SAT Inequalities Practice

When does an inequality sign reverse?

It reverses only when both sides are multiplied or divided by a negative quantity.

How can I check an inequality solution?

Substitute one value inside the solution region and one outside it into the original inequality.