Example 1 Easy
Which value satisfies both x > 3 and x < 8?
- 2
- 3
- 5
- 9
Show answer and explanation
Answer: 5
The value must be greater than 3 and less than 8. Only 5 works.
SAT Math skill page
SAT Systems of Inequalities Practice
Use multiple inequalities together to decide which values or choices satisfy every SAT constraint.
12-18 min practice time 3 examples on page Heart of Algebra
What this tests
What to know for this SAT skill
- Check whether a value satisfies multiple inequalities
- Translate paired constraints from word problems
- Find overlap between solution ranges
- Use boundary lines and shaded regions on graphs
Practice examples
Try a few SAT-style questions
Example 2 Medium
A number n must be at least 4 and less than 10. Which compound inequality represents this?
- 4 < n < 10
- 4 <= n < 10
- 4 <= n <= 10
- n <= 4 or n > 10
Show answer and explanation
Answer: 4 <= n < 10
At least 4 includes 4, and less than 10 excludes 10.
Example 3 Hard
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?
- 8 math, 10 reading
- 10 math, 10 reading
- 12 math, 8 reading
- 15 math, 5 reading
Show answer and explanation
Answer: 10 math, 10 reading
The pair has 20 questions and takes 10(2) + 10(1) = 30 minutes, satisfying both constraints.
Quick drills
Practice this skill from more angles
Check whether a value satisfies multiple inequalities
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Translate paired constraints from word problems
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Find overlap between solution ranges
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Use boundary lines and shaded regions on graphs
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Avoid these traps
Common mistakes on this skill
Solving before naming the task
The SAT often hides the real skill inside familiar wording. Identify the rule, relationship, or question type first.
Choosing an answer that only partly fits
Many wrong answers are close. Check every condition in the question before committing.
Skipping the final check
Reread what the question asks for so you do not answer a nearby but different question.
Study plan
How to practice this skill in Dolphin
- Read the question and name the tested skill before looking at the choices.
- Write the equation, rule, or passage relationship in plain language.
- Eliminate answers that violate the setup or overstate the evidence.
- Review misses by writing the exact trap that pulled you toward the wrong answer.
Related practice
Build the surrounding skills
Skill cluster
Keep practicing SAT Math
FAQ
Questions about SAT Systems of Inequalities Practice
What is the best way to practice SAT Systems of Inequalities Practice?
Start with a few focused examples, review the mistake pattern, then mix the skill into full SAT practice so you can recognize it in context.
Why does this skill matter on the SAT?
It shows up in short, high-leverage questions where one missed rule or setup can quickly cost a point.
Can Dolphin SAT help me drill this skill?
Yes. Dolphin SAT can surface targeted practice, track missed questions, and help you review the patterns that keep repeating.