Graphing Linear Inequalities Review

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 such as <, >, ≤, or ≥.

Front

What does the symbol ≤ represent in a linear inequality?

Back

The symbol ≤ indicates that the value on the left is less than or equal to the value on the right.

Front

What does the symbol < represent in a linear inequality?

Back

The symbol < indicates that the value on the left is strictly less than the value on the right.

Front

What is the significance of a closed circle on a number line?

Back

A closed circle indicates that the endpoint is included in the solution set, representing ≤ or ≥.

Front

What is the significance of an open circle on a number line?

Back

An open circle indicates that the endpoint is not included in the solution set, representing < or >.

Front

How do you graph a linear inequality in two variables?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region based on the inequality.

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.

Front

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

Back

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

Front

What is the difference between a system of inequalities and a single inequality?

Back

A system of inequalities consists of two or more inequalities that are considered together, while a single inequality involves only one inequality.

Front

How do you solve a system of linear inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the region where the shaded areas overlap; this region represents the solution set.