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'. It indicates 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'. It indicates that the value on the left is either less than or equal to the value on the right.

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

Front

What is the difference between a solid line and a dashed line in the graph of an inequality?

Back

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

Front

What does the graph of the inequality y > -x - 1 look like?

Back

The graph of y > -x - 1 is a region above the line y = -x - 1, which is dashed, indicating that points on the line are not included.

Front

How can you tell if a linear inequality has no solution?

Back

A linear inequality has no solution if the lines representing the inequalities are parallel and do not intersect.

Front

What is the solution set of the inequality x < 3?

Back

The solution set of the inequality x < 3 includes all real numbers less than 3.

Front

What does the term 'system of inequalities' mean?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph the inequality y ≤ 2x + 3?

Back

To graph y ≤ 2x + 3, first graph the line y = 2x + 3 as a solid line, then shade the region below the line.