Linear Inequalities Word Problem Practice

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.

Front

How do you represent a situation where a total cost must not exceed a certain amount?

Back

You can represent this situation using a linear inequality where the total cost is less than or equal to the specified amount.

Front

Write the inequality for the following situation: A band costs $150 per hour and a DJ costs $79 per hour. If the total cost must be less than or equal to $1200, what is the inequality?

Back

150x + 79y ≤ 1200, where x is the hours for the band and y is the hours for the DJ.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be either less than or equal to the value on the right.

Front

If you want to make at least $240 selling drinks, how would you express this as an inequality?

Back

x + 2y ≥ 240, where x is the number of hot chocolate glasses sold and y is the number of hot apple cider glasses sold.

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 or Ax + By ≥ C, where A, B, and C are constants.

Front

Write an inequality for the situation: You have at most 8 hours to spend at the mall and the beach.

Back

x + y ≤ 8, where x is the hours spent at the mall and y is the hours spent at the beach.

Front

What does the inequality 's ≤ 55' represent in a driving context?

Back

It represents that the speed 's' must be less than or equal to 55 miles per hour, indicating the maximum speed limit.

Front

How do you determine the feasible region for a system of linear inequalities?

Back

The feasible region is determined by graphing the inequalities on a coordinate plane and identifying the area where all the inequalities overlap.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means 'greater than' (not including the value), while '≥' means 'greater than or equal to' (including the value).