Writing Inequalities from Word Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you represent a word problem as an inequality?

Back

Identify the quantities involved, determine the relationship between them, and use appropriate inequality symbols to express the conditions.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the inequality 1.50x + 10 ≤ 40?

Back

Subtract 10 from both sides: 1.50x ≤ 30. Then divide by 1.50: x ≤ 20.

Front

What is the first step in writing an inequality from a word problem?

Back

Identify the total amount or limit that is being compared.

Front

In the inequality 4x + 7 ≥ 19, what does '4x' represent?

Back

'4x' represents four times a number, where 'x' is the unknown quantity.

Front

What is the solution to the inequality x + 5 < 10?

Back

Subtract 5 from both sides: x < 5.

Front

How do you interpret the inequality 125x + 55 < 600?

Back

It means that the total cost of hiring the DJ for 'x' hours plus the assistant's fee must be less than $600.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that satisfy the inequality, often resulting from contradictory statements.