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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you write an inequality from a word problem?

Back

To write an inequality from a word problem, identify the goal or limit, determine the variable representing the unknown, and express the relationship using inequality symbols (>, <, ≥, ≤).

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

In the context of saving money, how would you set up an inequality for a savings goal?

Back

Let x represent the number of weeks or units saved, then the inequality would typically be in the form of 'amount saved + (amount per week * x) ≥ savings goal'.

Front

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

Back

The first step in solving a two-step inequality is to isolate the term with the variable by performing the inverse operation (addition or subtraction) on both sides of the inequality.

Front

How do you interpret the solution of an inequality in a real-world context?

Back

The solution of an inequality represents a range of possible values that satisfy the condition, which can be interpreted in real-world terms, such as the minimum or maximum number of items or weeks needed.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values satisfy the original inequality, confirming that the solution is valid and applicable to the problem.

Front

How can you represent a situation where you need to save a certain amount of money over time?

Back

You can represent this situation with an inequality that includes the current amount saved, the amount saved per time period, and the total savings goal.

Front

What is the difference between '>' and '≥' in inequalities?

Back

The symbol '>' means 'greater than' and does not include the value itself, while '≥' means 'greater than or equal to', including the value.

Front

How do you solve the inequality 5x + 60 ≥ 200?

Back

First, subtract 60 from both sides to get 5x ≥ 140, then divide both sides by 5 to find x ≥ 28.