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 inequality x < 1 represent on a number line?

Back

The inequality x < 1 represents all numbers to the left of 1 on a number line, not including 1 itself.

Front

What does the inequality x ≥ -1 represent on a number line?

Back

The inequality x ≥ -1 represents all numbers to the right of -1 on a number line, including -1 itself.

Front

What is the difference between a solid line and a dashed line when 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, pick a test point not on the line (commonly (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What does the inequality x = 2 represent?

Back

The inequality x = 2 represents a vertical line on the graph where all points have an x-coordinate of 2.

Front

What is the solution set for the inequality x < 1?

Back

The solution set for the inequality x < 1 includes all real numbers less than 1.

Front

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

Back

The solution set for the inequality x ≥ -3 includes all real numbers greater than or equal to -3.

Front

How can you express the solution set of an inequality using interval notation?

Back

Interval notation uses brackets and parentheses to represent the solution set. For example, x < 1 is expressed as (-∞, 1) and x ≥ -3 is expressed as [-3, ∞).