4.5 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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the symbol '>' mean in a linear inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed line (for < or >) or solid line (for ≤ or ≥). 2. Shade the region 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 points on the line are not included in the solution (for < or >). A solid line indicates that points on the line are included (for ≤ or ≥).

Front

If the inequality is y < 2x + 3, what is the graph's shading direction?

Back

The shading will be below the line y = 2x + 3, indicating all points where y is less than 2x + 3.

Front

What is the solution set of a linear inequality?

Back

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 determine which side of the line to shade for the inequality y ≥ -rac{1}{2}x + 4?

Back

Choose a test point not on the line (e.g., (0,0)). If it satisfies the inequality, shade the side containing that point; otherwise, shade the opposite side.