Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the region that satisfies the inequality.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the values that satisfy the inequality, often visualized as a shaded region on a graph.

Front

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

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that the points on the line are not included (for < or >).

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

To determine which side to shade, you can test a point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the region containing that point; if not, shade the opposite side.

Front

What does the inequality x > 0 represent on a number line?

Back

The inequality x > 0 represents all real numbers greater than 0, which is shown as an open interval starting from 0 and extending to positive infinity.

Front

What does the inequality x = 2 represent?

Back

The inequality x = 2 represents a single point on the number line, specifically the point where x is exactly equal to 2.

Front

What does the inequality x = -3 represent?

Back

The inequality x = -3 represents a single point on the number line, specifically the point where x is exactly equal to -3.

Front

What does the inequality x = -1 represent?

Back

The inequality x = -1 represents a single point on the number line, specifically the point where x is exactly equal to -1.

Front

What is the graphical representation of the inequality x ≥ -3?

Back

The graphical representation of x ≥ -3 includes a solid line at x = -3 and shading to the right, indicating all values greater than or equal to -3.