A1.1.2.1 - Write, solve, and/or graph linear equations using various methods.


Key Vocabulary: Equation, Solve, Solution

A1.1.2.1.1 - Write, solve, and/or apply a linear equation (including problem situations).


Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday and made $65 in all. Which equation could be used to find t, the amount Jenny made in tips?
A. 65 = 4t + 8
B. 65 = 8t ÷ 4
C. 65 = 8t + 4
D. 65 = 8(4) + t

Answer: D


A1.1.2.1.2 - Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only.


One of the steps Jamie used to solve an equation is shown below.
–5(3x + 7) = 10
–15x + 35 = 10
Which statements describe the procedure Jamie used in this step and identify the property that justifies the procedure?
A. Jamie added –5 and 3x to eliminate the parentheses. This procedure is justified by the associative property.
B. Jamie added –5 and 3x to eliminate the parentheses. This procedure is justified by the distributive property.
C. Jamie multiplied 3x and 7 by –5 to eliminate the parentheses. This procedure is justified by the associative property.
D. Jamie multiplied 3x and 7 by –5 to eliminate the parentheses. This procedure is justified by the distributive property.
Answer: D

A1.1.2.1.3 - Interpret solutions to problems in the context of the problem situation. Note: Linear equations only.


Francisco purchased x hot dogs and y hamburgers at a baseball game. He spent a total of $10. The equation below describes the relationship between the number of hot dogs and the number of hamburgers purchased.
3x + 4y = 10
The ordered pair (2, 1) is a solution of the equation. What does the solution (2, 1) represent?
A. Hamburgers cost 2 times as much as hot dogs.
B. Francisco purchased 2 hot dogs and 1 hamburger.
C. Hot dogs cost $2 each and hamburgers cost $1 each.
D. Francisco spent $2 on hot dogs and $1 on hamburgers.
Answer: B

Additional Resources:

PDESAS Algebra I Module 1 Resources
Khan Academy - Linear Equations