Unit 2 review - linear inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥).

Front

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 solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

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

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 (above or below the line). Use a dashed line for < or > and a solid line for ≤ or ≥.

Front

What is the difference between a solution and a non-solution in the context of inequalities?

Back

A solution satisfies the inequality, meaning it makes the inequality true. A non-solution does not satisfy the inequality, making it false.

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 based on the context of the problem.

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What does it mean for a point to be 'not part of the solution set'?

Back

It means that when the coordinates of the point are substituted into the inequality, the inequality is not satisfied.

Front

What is the significance of the budget in a linear inequality problem?

Back

The budget represents a constraint that limits the values of the variables in the inequality, ensuring that the total cost does not exceed a specified amount.

Front

How do you interpret the inequality 7x + 13y ≤ 81?

Back

This inequality means that the total cost of x pizzas and y orders of breadsticks must be less than or equal to $81.