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' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to' and indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

How do you represent a situation where a variable must be greater than a certain value?

Back

You represent it using the '>' symbol, for example, x > 8 means x must be greater than 8.

Front

How do you represent a situation where a variable must be less than or equal to a certain value?

Back

You represent it using the '≤' symbol, for example, x ≤ 20 means x can be less than or equal to 20.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

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

Back

To solve -2x + 7 < 19, first subtract 7 from both sides to get -2x < 12, then divide by -2 (remember to flip the inequality sign) to get x > -6.

Front

What is a boundary point in the context of inequalities?

Back

A boundary point is a value that defines the limits of the solution set, often represented by the equality part of the inequality.