Writing and Solving Inequalities and Systems of Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing 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 '≥' represent?

Back

'≥' 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 '≤' represent?

Back

'≤' 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 system of inequalities?

Back

A system of inequalities is represented by two or more inequalities that share the same variables. For example: \(x + y \geq 20\) and \(10x + 20y \leq 280\).

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality is a shaded region on a coordinate plane that shows all the possible solutions that satisfy the inequality.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

Front

How do you solve a system of inequalities graphically?

Back

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

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line represents the values that make the inequality an equation. If the inequality is strict (>, <), the line is dashed; if it includes equality (≥, ≤), the line is solid.

Front

What is a feasible region in the context of inequalities?

Back

A feasible region is the area on a graph that satisfies all the inequalities in a system. It represents all possible solutions.

Front

How do you write an inequality for a word problem?

Back

Identify the variables, determine the constraints, and express the relationships using inequalities. For example, 'at least 20 tickets' translates to \(x + y \geq 20\).