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

When graphing a linear inequality with '≥' or '≤', what type of line is used?

Back

A solid line is used when graphing a linear inequality with '≥' or '≤' to indicate that points on the line are included in the solution.

Front

When graphing a linear inequality with '>' or '<', what type of line is used?

Back

A dashed line is used when graphing a linear inequality with '>' or '<' to indicate that points on the line are not included in the solution.

Front

How do you represent the inequality 'y < 3x' graphically?

Back

You would graph the line 'y = 3x' as a dashed line and shade below the line to represent all points where y is less than 3x.

Front

What is the solution set of the inequality 'y ≥ 2x + 1'?

Back

The solution set includes all points on or above the line represented by the equation 'y = 2x + 1'.

Front

What does the inequality 'y ≤ rac{1}{4}x + 2' represent graphically?

Back

It represents all points on or below the line 'y = rac{1}{4}x + 2', including the line itself.

Front

How do you determine if a point (x, y) is a solution to the inequality 'y > -x + 3'?

Back

Substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set; points on the line may or may not be included based on the inequality symbol.