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

How do you graph the inequality x ≥ -3?

Back

To graph x ≥ -3, draw a solid line at x = -3 and shade to the right, indicating all values greater than or equal to -3.

Front

What does the solution set x < 1 represent?

Back

The solution set x < 1 represents all values of x that are less than 1, which is shown by shading to the left of the line x = 1.

Front

How do you graph the inequality x > 0?

Back

To graph x > 0, draw a dashed line at x = 0 and shade to the right, indicating all values greater than 0.

Front

What does the solution set x = -3 represent?

Back

The solution set x = -3 represents only the single value -3, which is shown by a solid point on the line at x = -3.

Front

How do you graph the inequality x ≥ -3?

Back

To graph x ≥ -3, draw a solid line at x = -3 and shade to the right, indicating all values greater than or equal to -3.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the boundary value is included (≥ or ≤), while a dashed line indicates that the boundary value is not included (> or <).

Front

What does the inequality x < -3 mean?

Back

The inequality x < -3 means that x can take any value less than -3, which is represented by shading to the left of the line x = -3.

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 line (solid or dashed) to understand which values are included.