Graphing Inequalities

Front

What is an inequality in mathematics?

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 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph the inequality x ≤ 12 on a number line?

Back

To graph x ≤ 12, draw a number line, place a closed circle on 12 (indicating that 12 is included), and shade to the left to show all values less than or equal to 12.

Front

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

Back

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

Front

What is the difference between 'less than' (<) and 'less than or equal to' (≤)?

Back

'Less than' (<) means the value cannot equal the number, while 'less than or equal to' (≤) means the value can equal the number.

Front

What is the difference between 'greater than' (>) and 'greater than or equal to' (≥)?

Back

'Greater than' (>) means the value cannot equal the number, while 'greater than or equal to' (≥) means the value can equal the number.

Front

How do you graph the inequality x < 20 on a number line?

Back

To graph x < 20, draw a number line, place an open circle on 20 (indicating that 20 is not included), and shade to the left to show all values less than 20.

Front

How do you graph the inequality x ≥ 20 on a number line?

Back

To graph x ≥ 20, draw a number line, place a closed circle on 20 (indicating that 20 is included), and shade to the right to show all values greater than or equal to 20.

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 < 0 and x > 0 simultaneously.