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 include: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

How do you represent the inequality k < 3 on a number line?

Back

You would draw an open dot at 3 and shade to the left, indicating that k can take any value less than 3.

Front

What does a closed dot on a graph indicate?

Back

A closed dot indicates that the value at that point is included in the solution set, used for inequalities with ≤ or ≥.

Front

What does an open dot on a graph indicate?

Back

An open dot indicates that the value at that point is not included in the solution set, used for inequalities with < or >.

Front

How do you graph the inequality x ≥ 3?

Back

You would draw a closed dot at 3 and shade to the right, indicating that x can take any value greater than or equal to 3.

Front

What is the graphical representation of the inequality b ≤ -2?

Back

You would draw a closed dot at -2 and shade to the left, indicating that b can take any value less than or equal to -2.

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 determine the direction of shading when graphing an inequality?

Back

The direction of shading is determined by the inequality symbol: shade to the left for < or ≤, and shade to the right for > or ≥.

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.