Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) to show that one expression is not equal to the other.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '>' mean?

Back

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

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 3 means x is any number less than or equal to 3.

Front

What does the symbol '≥' mean?

Back

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

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle at 3 (indicating 3 is not included), and shade to the left to show all numbers less than 3.

Front

How do you solve the inequality -2x + 7 < 19?

Back

First, subtract 7 from both sides: -2x < 12. Then, divide by -2 (remember to flip the inequality sign): x > -6.

Front

What is the solution to the inequality 2x + 10 < 4x + 8?

Back

Rearranging gives: 2 < 2x, which simplifies to x > 1.

Front

What does the graph of x > -2 look like?

Back

The graph of x > -2 has an open circle at -2 (indicating -2 is not included) and shades to the right to show all numbers greater than -2.

Front

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

Back

'And' means both conditions must be true (intersection), while 'or' means at least one condition must be true (union).