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Simplify one-step inequalities to identify solution set

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Practice Inequalities with Addition and Subtraction

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Using GPA
Teacher Contributed

Real World Applications – Algebra I

Student Exploration

One of the most useful ways of using inequalities is calculating GPA. Many students use this as they’re figuring out which university or college they want to attend, and looking at their requirements.

You can use this college’s website to learn how to calculate your GPA: http://web.williams.edu/registrar/records/gpa.html

Upper division high school students can use inequalities to help them calculate what grades they need in some of their classes to raise their GPA. Let’s first look at one student’s grades and see if they’re eligible to attend a California State University (CSU). The required GPA for a CSU is 3.0. In the first two years, this student received the following grades:

When calculating GPA, we’re only using Semester grades. Try calculating this student’s grades on your own, using the numbers listed on the website. For the sake of applying for a 4-year university, let’s also not include grades from Advisory.

For 10th\begin{align*}10^{th}\end{align*} grade: (2.33+2+2.67+1.67+1.67+1.67+3.67+2.67+2.33+2)10=2.268\begin{align*}\frac{(2.33 + 2 + 2.67 + 1.67 + 1.67 + 1.67 + 3.67 + 2.67 + 2.33 + 2)}{10} = 2.268\end{align*}

For 9th\begin{align*}9^{th}\end{align*} grade: (2.67+2.33+2.33+2+2.67+2.67+2.33+2.67+2.67+2.33)10=2.467\begin{align*}\frac{(2.67 + 2.33 + 2.33 + 2 + 2.67 + 2.67 + 2.33 + 2.67 + 2.67 + 2.33)}{10} = 2.467\end{align*}

Total GPA: (2.268+2.467)2=2.3675\begin{align*}\frac{(2.268 + 2.467)}{2} = 2.3675\end{align*}

Using this information, we can calculate the types of grades that this student would need in order for him to be CSU-eligible. We can use the same setup to calculate these grades. So far, this student is not CSU-eligible, based on his grades. Let’s see what his grades in 11th\begin{align*}11^{th}\end{align*} grade would have to be in order for him to make the minimum. Let’s try to see if all B’s in all of his classes would make him eligible.

For 11th\begin{align*}11^{th}\end{align*} grade: (3×10)10=3.0\begin{align*}\frac{(3 \times 10)}{10} = 3.0\end{align*}

Total GPA for all three years: (3.0+2.268+2.467)3=2.578\begin{align*}\frac{(3.0 + 2.268 + 2.467)}{3} = 2.578\end{align*}

If this student had all B’s in his 11th\begin{align*}11^{th}\end{align*} grade year, he wouldn’t make the requirement. Let’s try to see what his 11th\begin{align*}11^{th}\end{align*} grade year GPA would have to be in order to make the minimum GPA requirement using an inequality.

Total GPA for all three years: (x+2.268+2.467)33.0\begin{align*}\frac{(x + 2.268 + 2.467)}{3} \ge 3.0\end{align*} let x\begin{align*}x\end{align*} represent 11th\begin{align*}11^{th}\end{align*} grade’s GPA

(x+4.735)3x+4.735x3.094.265\begin{align*}\frac{(x + 4.735)}{3} &\ge 3.0\\ x + 4.735 &\ge 9\\ x &\ge 4.265\end{align*}

This means that this student’s GPA for 11th\begin{align*}11^{th}\end{align*} grade year would have to be at least 4.265. Do you think this is possible? Why or why not? (Note: If high school students take classes at a community college or an Advanced Placement course, he/she can earn an additional 1 point for their final grades. i.e. A “B” grade would get calculated into the GPA as 4.0 instead of 3.0.)

Extension Investigation

If you are high school student, practice calculating what grades you should earn in order to get a minimum requirement GPA to get into a particular university of choice. Look on the university’s website! Each university’s requirements are different!

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