Compound Inequalities - Varsity Tutors

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Compound Inequalities

Study Guide

Key Definition

A compound inequality (or combined inequality) is two or more inequalities joined together with 'or' or 'and'.

Important Notes

  • To be a solution of an 'or' inequality, a value has to make only one part of the inequality true.
  • To be a solution of an 'and' inequality, it must make both parts true.
  • When two inequalities are joined with 'and', they are often written as a double inequality.

Mathematical Notation

$x \leq -3$ or $x > 2$ means x is less than or equal to -3 or x is greater than 2.Use ≤ or ≥ symbols correctly, and keep the variable in the middle for double inequalities.

Why It Works

Compound inequalities allow us to describe a range of solutions in a compact form.

Remember

Remember to apply operations on all parts of a compound inequality, not just two sides as in a normal inequality.

Quick Reference

Double Inequality:$-1 \leq x < 2$

Understanding Compound Inequalities

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Video explanation of this concept

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Beginner Explanation

A compound inequality (or combined inequality) is two or more inequalities joined together with 'or' or 'and'.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which statement is always true for every value of x that satisfies $-1 \leq x < 2$?

A$x$ is less than -1B$x$ is greater than 2C$x$ is equal to -1D$x$ is less than 2Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A teenager is allowed to watch TV if it's past 5 PM but before 10 PM. If T represents the time, write a compound inequality that represents this situation.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Write a compound inequality to represent all numbers x that are greater than or equal to -2 and less than or equal to 3.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which of the following is the solution for the compound inequality $-2 < x + 3 \leq 7$?

A$-5 < x \leq 4$B$-1 < x \leq 10$C$-5 < x < 4$D$-1 < x < 10$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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