Graphing Linear Inequalites

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 the symbol '>' represent?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Shade the region that satisfies the inequality.

Front

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

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates they are not included (< or >).

Front

If you have the inequality 2x + 3 < 7, what is the first step to solve it?

Back

Subtract 3 from both sides to isolate the term with x.

Front

What does flipping the inequality sign mean?

Back

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

Front

In the inequality 3x ≥ 12, do you need to flip the sign when dividing by 3?

Back

No, you do not need to flip the sign when dividing by a positive number.

Front

What is the solution set of the inequality x < 5?

Back

The solution set includes all real numbers less than 5.

Front

How do you determine which region to shade when graphing an inequality?

Back

Test a point not on the line (usually (0,0)) in the inequality. If it satisfies the inequality, shade the region containing that point.