## Practice Problems: Ugly Linear Equations

The title of this post reflects how I categorize problems. The solution to each of the following problems is 7. Focus on finding the most helpful series of algebraic steps to take someone reading your work from the problem as stated to the solution. As the problems begin to include more and more terms, be cautious about doing too much in any one step – as that is how errors often arise.

1.   $2(15-a)~=~4(a-3)$
2.   $b-9+3b~=~10+5b+50-8b-20$
3.   $3(m-1)-(m+3)~=~2(5-m)+(m+5)$
4. Continue reading Practice Problems: Ugly Linear Equations

## Practice Problems: Three Step Linear Equations

The solution to each of the following problems is 20. Focus on finding the most helpful three or four algebraic steps to take someone reading your work from the problem as stated to the solution.

1.   $3(x+10)~=~90$
2.   $2x-20~=~60-2x$
3.   $\dfrac{2x}{3}~=~\dfrac{60-x}{3}$
4. Continue reading Practice Problems: Three Step Linear Equations

## Practice Problems: Two Step Linear Equations

The solution to each of the following problems is 18. Focus on finding the most helpful algebraic steps to take a reader from the problem as stated to the solution.

1.   $2x+1~=~37$
2.   $5+3x~=~59$
3.   $2x+3x~=~90$
4. Continue reading Practice Problems: Two Step Linear Equations

## Practice Problems: One Step Linear Equations

The solution to each of the following twenty problems is 12. Focus on finding the most helpful algebraic step to take a reader from the problem as stated to the solution, and be sure you can explain why that step leads to a solution.

1.   $x+7~=~19$
2.   $3+x~=~15$
3.   $11~=~-1+x$
4. Continue reading Practice Problems: One Step Linear Equations

## Interactive Graphs for Linear, Quadratic, Rational, and Trig Functions Moved to GeoGebraTube

Some may have had trouble using my GeoGebra applets in their browsers. I have moved all of them to GeoGebraTube, which will hopefully fix the problem. You may search for them by typing “MathMaine” into the GeoGebraTube search box.

Links to all updated interactive graph applets are below. Comments and suggestions are always welcome!

Linear Functions

GeoGebraBook: Exploring Linear Functions, which contains:

Interactive Linear Function Graph: Slope-Intercept Form

## Analyzing Linear Equations: a summary

Towards the end of the unit(s) on Linear Equations and their graphs, students can feel a bit overwhelmed.  The following is an attempt to summarize and link the key concepts you need to be comfortable with.

### Lines

What is the least amount of information you need to Continue reading Analyzing Linear Equations: a summary