Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

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

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

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

Back

The symbol '<' means 'less than'. For example, y < 3 means y is less than 3.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, z ≥ 4 means z is greater than or equal to 4.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, a ≤ 7 means a is less than or equal to 7.

Front

How do you graph the inequality x < 4?

Back

You draw a number line, place an open dot at 4, and shade to the left to indicate all numbers less than 4.

Front

How do you graph the inequality y ≥ -2?

Back

You draw a number line, place a closed dot at -2, and shade to the right to indicate all numbers greater than or equal to -2.

Front

What is the difference between an open dot and a closed dot on a graph?

Back

An open dot indicates that the number is not included (for < or >), while a closed dot indicates that the number is included (for ≤ or ≥).

Front

What does the inequality b ≤ -2 represent on a graph?

Back

It represents all values of b that are less than or equal to -2, shown with a closed dot at -2 and shading to the left.

Front

How do you determine the solution set for the inequality a > 11?

Back

The solution set includes all values of a that are greater than 11, represented by an open dot at 11 and shading to the right.