Solutions to 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 (>, <, ≥, ≤).

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). Then shade the region that represents the solution set.

Front

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

Back

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

Front

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

Back

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

Front

Which of the following points is NOT a solution to the inequality y < 2? (0, 1), (0, 2), (-2, 0), (2, 0)

Back

(0, 2) is NOT a solution because it does not satisfy the inequality.

Front

Which of the following points is a solution to the inequality y ≥ -2? (0, 0), (0, 2), (-2, 0), (0, -2)

Back

(-2, 0) is a solution because it satisfies the inequality.

Front

Are points on the line part of the solution set for the inequality y ≤ mx + b?

Back

Yes, points on the line are part of the solution set because the inequality includes the equal sign.

Front

Are points on a dashed line part of the solution set for the inequality y < mx + b?

Back

False, points on a dashed line are NOT part of the solution set.

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality.