6C 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 solve the inequality 15 + 6x ≤ 100?

Back

Subtract 15 from both sides to get 6x ≤ 85, then divide by 6 to find x ≤ 14.17.

Front

What does the inequality 5x + 60 ≥ 200 represent in a word problem?

Back

It represents the situation where Sylvia is saving money and needs to find out how many weeks it will take her to reach her savings goal.

Front

What is the first step in solving the inequality -3y + 2 > 11?

Back

Subtract 2 from both sides to get -3y > 9.

Front

What does the solution x ≥ 28 mean in the context of saving money?

Back

It means Sylvia needs to save for at least 28 weeks to reach her goal of $200.

Front

How do you interpret the inequality x ≤ 15 in a real-world scenario?

Back

It indicates that Lea can wash a maximum of 15 cars to afford the headphones she wants.

Front

What is the significance of the term 'at least' in inequalities?

Back

'At least' indicates a minimum value that must be met or exceeded, often represented by a 'greater than or equal to' (≥) sign.

Front

What is the difference between 'greater than' (>) and 'greater than or equal to' (≥)?

Back

'Greater than' (>) means the value must be strictly more, while 'greater than or equal to' (≥) includes the value itself.

Front

How can you check if your solution to an inequality is correct?

Back

You can substitute the solution back into the original inequality to see if it holds true.

Front

What does the inequality y < -3 indicate about the value of y?

Back

It indicates that y must be less than -3, meaning any number smaller than -3 is a solution.