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.

$x+7~=~19$
$3+x~=~15$
$11~=~-1+x$
$3x~=~12+2x$
$x-2~=~10$
$-18+x~=~-6$
$9~=~x-3$
$-5x~=~-6x+12$
$2x~=~24$
$84~=~7x$
$x\cdot 5~=~60$
$36~=~x\cdot 3$
$\dfrac{x}{3}~=~4$
$6~=~\dfrac{x}{2}$
$\dfrac{1}{4}x~=~3$
$\dfrac{4}{3}~=~x \cdot \dfrac{1}{9}$

– 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:
Alicia is 15 years old. She is 3 years older than her younger brother Tony. How old is Tony?
Mahmoud has 24 apples. He has twice as many as Janice. How many apples does Janice have?
Gabriella’s immediate family has 8 family members. She has 4 fewer than Darius. How many immediate family members does Darius have?
Lawrence has 6 books. He has half as many as Aisha. How many books does Aisha have?