Review Linear Inequalities and systems of 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 '>' represent in a linear inequality?

Back

The symbol '>' indicates that the left side of the inequality is greater than the right side.

Front

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

Back

The symbol '≥' indicates that the left side of the inequality is greater than or equal to the right side.

Front

How do you write a linear inequality for a budget constraint?

Back

A budget constraint can be written as an inequality where the total cost of items is less than or equal to the budget.

Front

What is the standard form of a linear inequality?

Back

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

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

Front

What is the difference between '>' and '≥' in graphing?

Back

'>' uses a dashed line indicating that points on the line are not included, while '≥' uses a solid line indicating that points on the line are included.

Front

How do you interpret the solution of a system of inequalities?

Back

The solution of a system of inequalities is the region where the shaded areas of all inequalities overlap, representing all possible solutions.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph that satisfies all constraints of a system of inequalities.

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 coordinates of the point into the inequality and check if the statement is true.