Writing Linear Inequalities from 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 situation where a quantity cannot exceed a certain value?

Back

You use a 'less than or equal to' (≤) inequality. For example, if a person can spend no more than $40, it can be represented as x ≤ 40.

Front

What does the inequality 1.50x + 10 ≤ 40 represent in a word problem?

Back

It represents the total cost of rides (1.50 per ride) plus the admission fee (10) being less than or equal to $40.

Front

How do you write an inequality for a total amount that must not be exceeded?

Back

You write it as a 'less than or equal to' (≤) inequality. For example, if you have $14 to spend, the inequality would be 2d + 1p ≤ 14.

Front

What does the inequality s ≤ 18 indicate in a word problem?

Back

It indicates that the number of students (s) in the hall cannot exceed 18.

Front

How do you express a situation where a minimum amount is required?

Back

You use a 'greater than or equal to' (≥) inequality. For example, if at least $42 is needed, it can be represented as 3s + 2c ≥ 42.

Front

What is the significance of the inequality symbol '>'?

Back

The symbol '>' indicates that one quantity is strictly greater than another, meaning it cannot be equal.

Front

What does the inequality g ≤ 45 mean in a real-world context?

Back

It means that Grace has at most $45 in her purse, indicating she can have $45 or less.

Front

How do you determine the correct inequality from a word problem?

Back

Identify the key quantities and their relationships, then translate the conditions into an inequality using appropriate symbols.

Front

What is the difference between 'less than' (<) and 'less than or equal to' (≤)?

Back

'Less than' (<) means the quantity cannot equal the value, while 'less than or equal to' (≤) means it can equal the value.