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

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

Back

The symbol '>' means 'greater than'. For example, in the inequality y > 2x + 2, y is greater than the value of 2x + 2.

Front

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

Back

The symbol '<' means 'less than'. For example, in the inequality y < 2, y is less than 2.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, in the inequality y ≥ 2x + 2, y is greater than or equal to the value of 2x + 2.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, in the inequality y ≤ 2, y is less than or equal to 2.

Front

How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on the inequality symbol. Then shade the appropriate region of the graph that satisfies the inequality.

Front

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

Back

A dashed line indicates that the points on the line are not included in the solution (for < or >), while a solid line indicates that the points on the line are 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)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Front

What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

Front

How do you solve the inequality @@-rac{3}{15}x ge 4@@?

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