Inequalities and Compound Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 2 means x is greater than 2.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is less than 5.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 3 means x is greater than or equal to 3.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'.

Front

What does 'x > 2 or x ≤ -3' represent?

Back

This compound inequality means that x can be greater than 2 or less than or equal to -3.

Front

What does 'x < 1 and x > 5' represent?

Back

This compound inequality has no solution because no number can be less than 1 and greater than 5 at the same time.

Front

How do you solve the compound inequality '3x + 2 < -7 or -4x + 5 < 1'?

Back

To solve, isolate x in each inequality: 3x < -9 (x < -3) and -4x < -4 (x > 1). The solution is x < -3 or x > 1.

Front

What is the solution set for 'x > 4 or x < 10'?

Back

The solution set includes all real numbers because any number is either greater than 4 or less than 10.