Writing and Solving Inequalities and Systems of Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' mean?

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 represent a situation where a person has a limited budget using an inequality?

Back

You can represent it by letting a variable represent the amount spent and setting up an inequality that states the amount spent is less than or equal to the budget.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality by performing inverse operations.

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 dashed line (since it's not inclusive), then shade the area below the line.

Front

What does the solution to a system of inequalities represent?

Back

The solution to a system of inequalities represents all the points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the intersection of the solution sets of the individual inequalities.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The symbol '>' means 'greater than' and does not include the boundary, while '≥' means 'greater than or equal to' and includes the boundary.

Front

How do you write an inequality for a maximum limit?

Back

To write an inequality for a maximum limit, use the '≤' symbol to indicate that the value cannot exceed a certain amount.