Intro To Inequalities

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, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to'.

Front

How do you graph the inequality x ≥ 3 on a number line?

Back

You draw a number line, place a closed circle on 3, and shade to the right to indicate all numbers greater than or equal to 3.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.

Front

How do you solve the inequality 2x + 3 < 7?

Back

Subtract 3 from both sides to get 2x < 4, then divide by 2 to find x < 2.

Front

What is the solution set for the inequality x < 5?

Back

The solution set is all real numbers less than 5.

Front

How do you represent the solution of an inequality on a graph?

Back

You use a number line, with open circles for strict inequalities and closed circles for non-strict inequalities, shading the appropriate region.

Front

What does the inequality a ≥ 11 indicate about the value of a?

Back

It indicates that a can be 11 or any number greater than 11.

Front

How do you combine inequalities?

Back

You can combine inequalities using logical operators; for example, if a < b and b < c, then a < c.