Writing Inequalities with Variables on Both Sides

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that they are not equal, using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

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

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'fewer than' or 'less than'.

Front

How do you write an inequality for Norah's earnings from the tooth fairy compared to Kate's?

Back

0.75x ≥ 1.25 + 0.25x, where x is the number of teeth lost.

Front

What is the first step to solve the inequality 0.75x ≥ 1.25 + 0.25x?

Back

Subtract 0.25x from both sides to isolate terms with x.

Front

What is the cost equation for the first rental car agency?

Back

Cost = 30 + 0.15x, where x is the number of miles driven.

Front

What is the cost equation for the second rental car agency?

Back

Cost = 36 + 0.10x, where x is the number of miles driven.

Front

How do you determine when two rental car agencies cost the same?

Back

Set their cost equations equal to each other: 30 + 0.15x = 36 + 0.10x.

Front

What is the meaning of 'not equal' in the context of inequalities?

Back

'Not equal' indicates that the two expressions being compared do not have the same value.

Front

Write an inequality for Katie's taxi ride cost if she has no more than $10 to spend.

Back

1.75 + 0.65m < 10, where m is the number of miles.