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SAT Math skill page

SAT Systems of Inequalities Practice

Use multiple inequalities together to decide which values or choices satisfy every SAT constraint.

Practice systems of inequalities in Dolphin SATPractice questions
12-18 min practice time3 questions on pageHeart of Algebra
Practice time12-18 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
Which value satisfies both x > 3 and x < 8?
  1. 2
  2. 3
  3. 5
  4. 9
Show answer and solution
Correct answerC. 5

Solution walkthrough

  1. The value must be greater than 3 and less than 8.
  2. Only 5 works.
Question 2 of 3Medium
A number n must be at least 4 and less than 10. Which compound inequality represents this?
  1. 4 < n < 10
  2. 4 <= n < 10
  3. 4 <= n <= 10
  4. n <= 4 or n > 10
Show answer and solution
Correct answerB. 4 <= n < 10

Solution walkthrough

  1. At least 4 includes 4, and less than 10 excludes 10.
Question 3 of 3Hard
A student needs at least 20 total practice questions and wants to spend no more than 30 minutes. If math questions take 2 minutes and reading questions take 1 minute, which pair works?
  1. 8 math, 10 reading
  2. 10 math, 10 reading
  3. 12 math, 8 reading
  4. 15 math, 5 reading
Show answer and solution
Correct answerB. 10 math, 10 reading

Solution walkthrough

  1. The pair has 20 questions and takes 10(2) + 10(1) = 30 minutes, satisfying both constraints.

Avoid these traps

Common mistakes on this skill

Accepting a point that satisfies only one inequality

A solution to a system must lie in the overlap and satisfy every inequality simultaneously.

Using the wrong boundary style

Use a solid boundary for <= or >= and a dashed boundary for < or >.

Study plan

How to practice this skill in Dolphin

  1. Graph each boundary line and decide whether that boundary is included.
  2. Use a test point to determine the correct side of each boundary.
  3. Identify the overlap and substitute the requested point into every original inequality.
Practice systems of inequalities in Dolphin SAT

Related practice

Build the surrounding skills

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

Skill cluster

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FAQ

Questions about SAT Systems of Inequalities Practice

What is the solution to a system of inequalities?

It is the set of points that satisfies all inequalities in the system at the same time.

How do I choose which side of a line to shade?

Substitute a test point not on the line. Shade the side containing it only if the inequality is true.