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