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.   $50~=~4(x-5)-10$
5.   $x~=~\dfrac{100-2x}{3}$
6.   $25-\dfrac{1}{4}x~=~x$
7.   $2(x-10)-5~=~15$
8.   $\dfrac{3x}{2}-5~=~x+5$
9.   $4x-5~=~95-x$
10.   $12~=~\dfrac{4x-20}{5}$
11.   $-\dfrac{x+6}{2}~=~7-x$
12.   $-x~=~4-\dfrac{6}{5}x$
13.   $9-\dfrac{x}{2}~=~-1$

– Read each of the following, and decide on a variable you will use to answer the question.
– Then write an algebraic equation that describes the situation using the variable you chose.
– Then solve for the variable to answer the question:

14. If Jimena has sixty three manga books, which is three times nineteen less than twice what Derrick has, how many manga books does Derrick have?
15. Three friends collect athletic shoes. Esteban and Zuri have both collected the same number of athletic shoes. Esteban has ten fewer than three times Duong’s collection, while Zuri’s collection size is one hundred thirty pairs diminished by four times Duong’s collection. How many pairs are in Duong’s collection?