Inequalities Word Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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 'less than or equal to'.

Front

How do you represent a situation where a total must be less than a certain amount?

Back

You use an inequality with the 'less than' symbol (<) to represent that the total must be below a specified value.

Front

How do you represent a situation where a total must be at least a certain amount?

Back

You use an inequality with the 'greater than or equal to' symbol (≥) to indicate that the total must meet or exceed a specified value.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

How do you solve the inequality 5x + 10 ≥ 100?

Back

Subtract 10 from both sides to get 5x ≥ 90, then divide by 5 to find x ≥ 18.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality on a number line involves shading the region that represents all possible solutions, using an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is a real-world example of using inequalities?

Back

A real-world example is budgeting, where you might need to ensure that your expenses do not exceed your income.