Solving Linear Inequalities Word Problems

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 ≥). It represents a range of possible solutions rather than a single solution.

Front

How do you represent a word problem as a linear inequality?

Back

Identify the quantities involved, assign variables, determine the relationship between them, and express the conditions using inequality symbols.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than 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 can be smaller than or equal to the value on the right side.

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 can be larger than or equal to the value on the right side.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

Front

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

Back

The first step is to read the problem carefully, identify the variables, and determine what is being asked.

Front

In the problem 'Mona is ordering cups...', what does '3.5x + 14 < 0.5x + 22' represent?

Back

This inequality represents the condition that the total cost of cups from Company A must be less than the total cost from Company B.

Front

In the taxi cab problem, what does '0.75n + 1.75 ≤ 20' represent?

Back

This inequality represents the condition that the total cost of the taxi ride must be less than or equal to $20.