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

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph the inequality r ≥ -6 on a number line?

Back

To graph r ≥ -6, draw a number line, place a closed circle on -6 (indicating that -6 is included), and shade to the right to indicate all numbers greater than -6.

Front

What does the inequality x < -4 mean?

Back

The inequality x < -4 means that x can take any value less than -4.

Front

How do you solve the inequality x + 5 > 10?

Back

To solve x + 5 > 10, subtract 5 from both sides to get x > 5.

Front

What is the solution to the inequality 5 - 3x < -4?

Back

To solve 5 - 3x < -4, subtract 5 from both sides to get -3x < -9, then divide by -3 (remember to flip the inequality sign) to get x > 3.

Front

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

Back

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

Front

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

Back

The solution set of an inequality is represented on a number line by using open circles for strict inequalities and closed circles for non-strict inequalities, along with shading to indicate the range of solutions.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that satisfy the inequality, such as x < x.