## Solve This #1 – Wrap Up

*September 23, 2011 at 8:53 am* *
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This was pretty interesting. I posted a blog asking for solutions to a problem, and got a lot of feedback.

Colleen Young (@ColleenYoung on Twitter) in the comments & Colin Graham (@ColinTGraham on Twitter) on Twitter used a graphical approach. They graphed and noted where the function was between 2 & 9.

David Radcliffe (@daveinstpaul on Twitter) and Liz Durkin (@LizDK on Twitter) both used an algebraic approach that was right on the money.

Shawn Urban (@stefras on Twitter) used a unique algebraic approach as shown in the blog post Algebra 2: Solving Absolute Value Equations by Kate Nowak (@k8nowak on Twitter). I hadn’t really seen that before, and liked it a great deal. I may work it in next semester when solving absolute value equations/inequalities.

**My Solution**

What jumped out to me was a graphical approach as well. I thought about graphing the parabola , and then determining where the function was between 2 & 9 and between -9 & -2.

All that remains at that point is finding the endpoints of the interval algebraically.

Of course, I imagine many students might initially miss the problem at x = 0.

**Second Solution**

Another approach that came to me was to initially solve the inequality , and then taking out the solutions to . These two inequalities are quite easy to solve algebraically as they are intersections as opposed to unions.

In other words, I’d start with and then delete the intervals and .

**Summary**

I think this can be a fun feature of the blog. I will try to work it in on a regular basis. If you have any ideas for problems to include, let me know. I also welcome comments on my two approaches to this problem.

– George

*I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.*

Entry filed under: General Teaching, Math. Tags: absolute value inequalities, algebra, developmental math, george woodbury, intermediate algebra, Math, math teachers, solve this, teaching, woodbury.

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