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 such as <, >, ≤, or ≥.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality with '≥' or '≤'?

Back

You draw a solid line to represent the boundary, and shade the region that satisfies the inequality.

Front

How do you graph a linear inequality with '>' or '<'?

Back

You draw a dashed line to represent the boundary, and shade the region that satisfies 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

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 (for '≥' or '≤'), while a dashed line indicates that points on the line are not included (for '>' or '<').

Front

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

Back

You can test a point not on the line (like (0,0)) in the inequality. If it satisfies the inequality, shade the side containing that point.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What is an example of a linear inequality?

Back