Solving and Graphing 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 '<' represent in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 8 means x is any number less than 8.

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 6 means x is any number greater than 6.

Front

How do you graph the inequality x < 8?

Back

To graph x < 8, draw a number line, place an open circle at 8, and shade to the left to indicate all numbers less than 8.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, r ≥ -6 means r can be any number greater than or equal to -6.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

To solve 10 ≥ x - 3, add 3 to both sides to get 13 ≥ x, which can be rewritten as x ≤ 13.

Front

What is the solution set for the inequality x > 6?

Back

The solution set for x > 6 includes all real numbers greater than 6.

Front

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

Back

The solution of an inequality is represented on a number line using open circles for '<' or '>' and closed circles for '≤' or '≥', along with shading in the appropriate direction.

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 k < 3?

Back

The solution to k < 3 includes all real numbers less than 3.