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 (e.g., <, >, ≤, ≥).

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

Are points on a solid line part of the solution set?

Back

Yes, points on a solid line are part of the solution set.

Front

Are points on a dashed line part of the solution set?

Back

No, points on a dashed line are NOT part of the solution set.

Front

What does it mean if a linear inequality is represented with a dashed line?

Back

A dashed line indicates that the points on the line are not included in the solution set.

Front

What does it mean if a linear inequality is represented with a solid line?

Back

A solid line indicates that the points on the line are included in the solution set.

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the significance of the shaded region in a graph of a linear inequality?

Back

The shaded region represents all the solutions to the inequality.

Front

If the inequality is y < 2x + 3, what type of line is used to graph it?

Back

A dashed line is used because the inequality does not include equality.

Front

If the inequality is y ≥ -x + 1, what type of line is used to graph it?

Back

A solid line is used because the inequality includes equality.