Word Problems Involving Linear Inequalities in Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants and x and y are variables.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side of the inequality is either greater than or equal to the value on the right side.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side of the inequality is either less than or equal to the value on the right side.

Front

How do you represent a situation where spending must be less than a certain amount using a linear inequality?

Back

You represent it by using the 'less than' symbol (<) or 'less than or equal to' symbol (≤) in the inequality.

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

In the context of word problems, what does 'at least' indicate when forming a linear inequality?

Back

'At least' indicates that the value must be greater than or equal to a certain amount, which is represented by the symbol '≥'.

Front

In the context of word problems, what does 'no more than' indicate when forming a linear inequality?

Back

'No more than' indicates that the value must be less than or equal to a certain amount, which is represented by the symbol '≤'.

Front

How do you determine the variables in a linear inequality word problem?

Back

Identify the quantities that can change or vary in the problem, and assign a variable (like x or y) to represent each of these quantities.

Front

What is the first step in solving a word problem involving linear inequalities?

Back

The first step is to read the problem carefully and identify the key information, including the quantities involved and the relationships between them.

Front

How do you graph a linear inequality on a coordinate plane?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.