Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or equal to a specified number.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. It indicates that a value is smaller than a specified number.

Front

How do you graph the inequality x < 1?

Back

To graph x < 1, draw a number line, place an open circle at 1 (not including 1), and shade to the left to show all numbers less than 1.

Front

How do you graph the inequality x ≥ 2?

Back

To graph x ≥ 2, draw a number line, place a closed circle at 2 (including 2), and shade to the right to show all numbers greater than or equal to 2.

Front

What is the solution set for the inequality x > -3?

Back

The solution set for x > -3 includes all numbers greater than -3, represented as (-3, ∞) on a number line.

Front

What does the solution set x = 2 represent?

Back

The solution set x = 2 represents a single point on the number line where x is exactly equal to 2.

Front

How do you determine the solution set from a graph?

Back

To determine the solution set from a graph, identify the shaded region and the type of circle (open or closed) at the boundary point.

Front

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

Back

An open circle indicates that the number is not included in the solution (e.g., x < 1), while a closed circle indicates that the number is included (e.g., x ≥ 1).

Front

What does the inequality x < 2 look like on a number line?

Back

The inequality x < 2 is represented by an open circle at 2 and shading to the left, indicating all numbers less than 2.