Practice: Ugly Linear Equation Problems

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: Ugly Linear Equation Problems

Practice: Three Step Linear Equation Problems

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: Three Step Linear Equation Problems

Practice: One Step Linear Equation Problems

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: One Step Linear Equation Problems