Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent a word problem as an inequality?

Back

Identify the quantities involved, determine the relationships (greater than, less than, etc.), and translate the conditions into an inequality.

Front

What does the inequality 5x + 10 ≥ 100 represent in a word problem context?

Back

It represents a situation where a person needs to earn at least $100, with $5 earned per hour and an initial amount of $10.

Front

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

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

How can you express the condition 'less than 180 days left of school' mathematically?

Back

This can be expressed as d < 180, where d represents the number of days left.

Front

What is the significance of the inequality x + y < 10 in a word problem?

Back

It indicates that the total number of items (x and y) must be less than 10, often representing a limit or constraint.

Front

What does the inequality 2x + 3y ≥ 20 signify in a basketball challenge context?

Back

It signifies that the total points scored from 2-point shots (x) and 3-point shots (y) must be at least 20.

Front

How do you interpret the inequality x + y ≤ 14 in a work hours context?

Back

It indicates that the total hours worked at two jobs (x and y) cannot exceed 14 hours.

Front

What does the inequality 8x + 25y ≥ 100 represent in a saving scenario?

Back

It represents the condition that the total amount saved from two jobs must be at least $100.

Front

What is the meaning of the inequality x + y < 10 in a sports team context?

Back

It indicates that the total number of players (x and y) on a team must be less than 10.