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.

$2x+1~=~37$
$5+3x~=~59$
$2x+3x~=~90$
$2x~=~-4x+108$
$54~=~2x+x$
$92-20~=~4x$
$2(x-7)~=~22$
$39~=~(-5+x)\cdot3$
$33-15~=~10x-9x$
$12~=~\dfrac{2x}{3}$
$10~=~4+\dfrac{x}{3}$
$\dfrac{x+6}{4}~=~6$

– 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:
Hector has 20 songs on his phone, which matches what Thea gets if she doubles the number of songs on her phone and reduces the result by 16. How many songs does Thea have on her phone?
Aleena has two photographs in her room, which is a tenth of two more than the number Leon has in his room. How many photographs does Leon have in his room?
Pedro has just started collecting Pokemon cards, while Amira has already collected 66 of them. If Pedro’s card count is increased by four, and this quantity is tripled, he will have as many as Amira. How many Pokemon cards does Pedro have?