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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the expression on the left is greater than or equal to the expression on the right.

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

To determine if a point is part of the solution set, 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 a solid line and a dashed line in the graph of an inequality?

Back

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

Front

How do you graph the inequality y > 2x + 1?

Back

To graph y > 2x + 1, first graph the line y = 2x + 1 as a dashed line, then shade the area above the line to represent all points where y is greater than 2x + 1.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What does the solution set of a system of linear inequalities represent?

Back

The solution set of a system of linear inequalities represents all the points that satisfy all inequalities in the system simultaneously.

Front

How can you tell if a system of linear inequalities has no solution?

Back

A system of linear inequalities has no solution if the graphs of the inequalities do not intersect or overlap at any point.

Front

What is the graphical representation of the inequality 5x + y ≤ -1?

Back

To graph 5x + y ≤ -1, first graph the line 5x + y = -1 as a solid line, then shade the area below the line to represent all points where 5x + y is less than or equal to -1.

Front

What is the meaning of the term 'solution set' in the context of linear inequalities?

Back

The solution set is the collection of all ordered pairs (x, y) that satisfy the given linear inequality.