Let's Review
Earlier in this course, you learned how to write linear inequalities from descriptions. These kinds of inequalities have two variables, usually \(x\) and \(y\). You can write linear inequalities by defining what your variables represent, determining which inequality symbol to use, and then putting it all together to write the inequality.
Since there is more than one inequality symbol to choose from, it is important that you look for key words and phrases in the scenario description so that you pick the correct one. Some key words and phrases are shown in the table below.
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\( ( \lt ) \) Less Than |
\( ( \leq ) \) Less Than or Equal To |
\( ( \gt ) \) Greater Than |
\( ( \geq ) \) Greater Than or Equal To |
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Review the example below to refresh your memory about how to write linear inequalities.
Eva is saving tickets to earn a prize at the arcade; she needs a minimum number of tickets to buy this prize. She has 285 tickets now and wins an average of 50 tickets each time she visits the arcade.
Write a linear inequality to represent this scenario.
The steps for writing a linear equality from a description are shown in the table below. Click each step to see it applied to the example.
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Let \(x =\) the number of visits Eva needs to make to the arcade to earn tickets. Let \(y =\) the number of tickets earned. |
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Since the problem description contains the key word minimum use the symbol \(\geq\). |
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You know that Eva already has 285 tickets and that she earns an average of 50 tickets per visit. The symbol to use is \(\geq ,\) and the variables are \(x\) and \(y\). Then, \(y \geq 50x + 285\) |
Use the activity below to practice the process of writing a linear inequality. You will need the description below to answer the questions.
A ride-sharing service charges $7.50 plus $1.25 per mile driven. Tori can spend no more than a certain amount of money on ride sharing each month.
Answer the question on each slide, then check your answer.
