Algebra - Chapter 5 Flashcard Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include <, >, ≤, and ≥.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

What does the symbol '<' mean in inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.

Front

What does the symbol '≤' mean in inequalities?

Back

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

Front

How do you solve the compound inequality 2 < x + 2 < 5?

Back

To solve, subtract 2 from all parts: 0 < x < 3.

Front

What is the solution set for the inequality x ≥ 2 and x ≤ 4?

Back

The solution set is the interval [2, 4], meaning x can take any value from 2 to 4, inclusive.

Front

What is the solution set for the inequality x > 2 or x ≤ -3?

Back

The solution set includes all values greater than 2 and all values less than or equal to -3.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

Front

How do you graph the inequality y < -1?

Back

To graph y < -1, draw a horizontal dashed line at y = -1 and shade the area below the line.