Two Step Inequality Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you represent a situation where a person needs to earn at least a certain amount of money?

Back

You can represent this situation with an inequality using the 'greater than or equal to' symbol (≥). For example, if a person needs to earn at least $50, you would write: earnings ≥ 50.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater than or equal to the value on the right side.

Front

How do you write an inequality for a situation where you have a fixed amount of money and want to spend less than that amount?

Back

You would use the 'less than' symbol (<). For example, if you have $50 and want to spend less, you would write: spending < 50.

Front

What is the first step in solving a two-step inequality?

Back

The first step is to isolate the term with the variable by performing the opposite operation (addition or subtraction) on both sides of the inequality.

Front

What is the second step in solving a two-step inequality?

Back

The second step is to isolate the variable by performing the opposite operation (multiplication or division) on both sides of the inequality.

Front

How do you interpret the solution of an inequality?

Back

The solution of an inequality represents a range of values that satisfy the condition. For example, if x > 5, any number greater than 5 is a solution.

Front

What is an example of a real-world situation that can be modeled with a two-step inequality?

Back

A real-world situation could be budgeting for a party where you need to spend less than a certain amount while considering fixed costs and variable costs.

Front

How do you check if a solution to an inequality is correct?

Back

You can check by substituting the solution back into the original inequality to see if it makes the inequality true.

Front

What does the term 'variable' mean in the context of inequalities?

Back

A variable is a symbol (often x or y) that represents an unknown value in an inequality.