Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates 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 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

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 can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

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

How can 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, the point is part of the solution set.

Front

What is the difference between 'strict' and 'non-strict' inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Front

What is the graphical representation of y < 2/5x + 1?

Back

The graph is a dashed line representing the equation y = 2/5x + 1, with the area below the line shaded.

Front

What does the solution to the inequality x < -1 look like on a number line?

Back

On a number line, the solution x < -1 is represented by an open circle at -1 and a shaded line extending to the left.

Front

How do you solve a system of linear inequalities?

Back

To solve a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap.