# 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.   $\dfrac{4c-12+c+1}{2}~=~c+5$
5.   $\dfrac{4d}{-3}~=~\dfrac{28}{6}-2d$
6.   $\dfrac{x-7}{6}~=~\dfrac{7-x}{2}$
7.   $\dfrac{11a-22}{11}+a-1~=~\dfrac{36-2a}{2}$
8.   $w+\dfrac{w-16}{5}~=~\dfrac{3}{5}w+8-w$
9.   $\dfrac{v-5}{2}-\dfrac{1}{4}~=~\dfrac{5}{2}-\dfrac{v}{4}$
10.   $\dfrac{t+3}{2}+3t-\dfrac{10t+11}{7}~=~\dfrac{13t+10}{7}$
11.   $\dfrac{-15+y}{6}+\dfrac{1-3y}{3}~=~-\dfrac{4(1+2y)}{3}+y+5$
12.   $\dfrac{x-10}{5}+\dfrac{1}{7}~=~\dfrac{3-x}{7}+\dfrac{4}{35}$
13.   $\dfrac{d+5}{4}+\dfrac{2}{3}d-1~=~\dfrac{87-d}{12}$
14.   $\dfrac{2w-10}{5}-\dfrac{10-4w}{3}~=~6-\dfrac{4}{15}(w-10)$
15.   $\dfrac{a+2}{7}+\dfrac{1}{10}(a+3)-\dfrac{3-a}{5}~=~\dfrac{a+2}{14}-\dfrac{2-4a}{35}+\dfrac{17}{70}a$