Writing and Graphing 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

How do you represent 'at least' in an inequality?

Back

'At least' is represented by the symbol '≥' (greater than or equal to). For example, 'at least 25' is written as c ≥ 25.

Front

What does the inequality x < 9 represent?

Back

The inequality x < 9 means that x can take any value less than 9.

Front

How is 'at most' represented in an inequality?

Back

'At most' is represented by the symbol '≤' (less than or equal to). For example, 'at most 45' is written as g ≤ 45.

Front

What does the inequality c > 250 indicate?

Back

The inequality c > 250 indicates that c can take any value greater than 250.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' is represented by '>' and does not include the value itself, while 'greater than or equal to' is represented by '≥' and includes the value.

Front

How do you graph the inequality x < 9 on a number line?

Back

To graph x < 9, draw an open circle at 9 (indicating that 9 is not included) and shade to the left to show all values less than 9.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

How do you interpret the inequality g ≤ 45 in a real-world context?

Back

The inequality g ≤ 45 means that the amount of money Grace has in her purse is 45 dollars or less.

Front

What is the significance of the open circle in graphing inequalities?

Back

An open circle indicates that the number at that point is not included in the solution set of the inequality.