Question Video: Writing and Solving Linear Inequalities in a Real-World Context

Video Transcript

Daniel wants to buy groceries. He wants to have at least 80 dollars cash with him. And he currently has 15 dollars. Write and solve an inequality that would determine how much cash Daniel should withdraw from the bank.

Daniel wants at least 80 dollars cash. To find out what kind of inequality we should write, let’s think about this. Would it be okay if Daniel had more than 80 dollars cash? Yes. Would it be okay if Daniel had exactly 80 dollars cash? Yes. It would not be okay if he had less than 80 dollars cash. And that means we need an inequality symbol that represents more or equal. We need the money Daniel has to be greater than or equal to 80 dollars. And the money Daniel has consists of two pieces. The money he should withdraw and the 15 dollars he already has. Together, these two values should be greater than or equal to 80 dollars. We can let the variable 𝑥 represent the money that Daniel will withdraw. And so we’re saying that 𝑥 plus 15 must be greater than or equal to 80.

At this point, we have successfully written an inequality to show the money that Daniel needs. But we need to continue by solving this inequality. We want to solve for what values of 𝑥 would this statement be true. And we do that by subtracting 15 dollars from both sides of the inequality. 80 dollars minus 15 dollars equals 65 dollars. 𝑥 must be greater than or equal to 65. And our 𝑥 represents the money that he should withdraw from the bank. Daniel must withdraw at least 65 dollars if he wants to have 80 dollars cash with him. And so an inequality that we’ve written 𝑥 plus 15 is greater than or equal to 80 and solved for 𝑥 must then be greater than or equal to 65.