Unit 2 review - 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 (such as <, >, ≤, or ≥).

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

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system when substituted into them.

Front

What does the symbol '≤' represent 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 '≥' represent 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 write a linear inequality from a word problem?

Back

Identify the variables, determine the relationship between them, and express the constraints using inequality symbols.

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.

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What is the significance of the solution set of a linear inequality?

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The solution set represents all possible values of the variables that satisfy the inequality, often visualized as a shaded region on a graph.

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What does it mean if a system of inequalities has no solution?

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A system of inequalities has no solution if there is no set of values that satisfies all inequalities simultaneously.

Front

What does it mean if a system of inequalities has an infinite number of solutions?

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A system of inequalities has an infinite number of solutions if there are multiple sets of values that satisfy all inequalities, often represented by a region on a graph.

Front

How can 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.