2.1 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

What symbols are used to represent inequalities?

Back

The symbols used to represent inequalities are: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

What does an open dot represent when graphing inequalities?

Back

An open dot represents that the value at that point is not included in the solution set, used for < and >.

Front

What does a closed dot represent when graphing inequalities?

Back

A closed dot represents that the value at that point is included in the solution set, used for ≤ and ≥.

Front

How do you graph the inequality x < 5?

Back

To graph x < 5, place an open dot at 5 on the number line and shade to the left to indicate all values less than 5.

Front

How do you graph the inequality x ≤ 3?

Back

To graph x ≤ 3, place a closed dot at 3 on the number line and shade to the left to indicate all values less than or equal to 3.

Front

What is the inequality that represents 'A healthy daily diet contains no more than 24 grams of sugar'?

Back

The inequality is x ≤ 24, where x represents the grams of sugar.

Front

What is the inequality that represents 'The maximum score on the pilot's test is 95 points'?

Back

The inequality is p ≤ 95, where p represents the score on the pilot's test.

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 2x + 3 > 7?

Back

To solve 2x + 3 > 7, subtract 3 from both sides to get 2x > 4, then divide by 2 to find x > 2.