Solving and Graphing Linear Inequalities

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 (e.g., <, >, ≤, ≥).

Front

What does it mean to solve a linear inequality?

Back

To solve a linear inequality means to find all values of the variable that make the inequality true.

Front

When solving an inequality, when do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Shade the region that satisfies the inequality.

Front

What does a dashed line indicate in the graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution (for < or > inequalities).

Front

What does a solid line indicate in the graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution (for ≤ or ≥ inequalities).

Front

If the inequality is y < mx + b, which direction do you shade?

Back

You shade below the line.

Front

If the inequality is y > mx + b, which direction do you shade?

Back

You shade above the line.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you represent an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade in the direction of the solution.