A.REI.1 [576524]
Student
Class
Date
1.
The steps below are used to solve the equation
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Which of the following statements is correct?
A. Step 1 is the result of applying the associative property of
multiplication to the given equation.
B. Step 1 is the result of applying the associative property of addition to
the given equation.
C. Step 3 is the result of applying the commutative property to the
equation in step 2.
D. Step 3 is the result of applying the distributive property to the
equation in step 2.
A.REI.1
Page 1/10
2.
The equation
can be used to convert temperature from
degrees Fahrenheit
to degrees Celsius
first step in solving the equation for
Which of these could be the
A.
B.
C.
D.
3. Jacob stated that he solved the equation
using the addition and
multiplication property of equality. Which statement is true?
A.
Jacob added
to both sides and multiplied both sides by
B. Jacob added
to both sides and multiplied both sides by
C.
Jacob added to both sides and multiplied both sides by
A.REI.1
Page 2/10
D. Jacob added to both sides and multiplied both sides by
4. Martin and his sister started a new tutoring business. They rent an office
for $760 per month and charge $120 per student per month.
Part A: Write an equation to represent the monthly profit they make for
tutoring x students.
Part B: If they made a profit of $200 in the first month, solve the
equation in part A to find the value of x. Justify each step by writing the
property or reason next to it.
Use words, numbers, and/or pictures to show your work.
5. Michaela is learning to solve algebraic equations by applying the
mathematical properties of equality. She had to solve the equation
below.
Michaela wrote down the steps she took to solve the equation
Steps taken to solve the equation
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
A.REI.1
Page 3/10
Step 8:
Step 9:
Why does the equation found at step 4 preserve the equality asserted by
the equation found at step 3?
A. The sum of a number and its additive inverse is 0.
B. The product of a number and its multiplicative inverse is 1.
C. The equality of numbers will not change when a constant is added to
one side of an equation and the additive inverse of the constant is
added to the other side of the equation.
D. The equality of numbers will not change when one side of an equation
is multiplied by a constant and the other side of the equation is
multiplied by the multiplicative inverse of the constant.
6. The charges, C, in dollars from a taxi company for traveling a distance of
x miles is represented by the equation
Which of the following is a
possible step and valid explanation for the process of solving for x in
terms of C?
A.
The subtraction equality property must first be used to
transform the equation in terms of the miles traveled.
B.
The distributive property must first be used to simplify
the charge equation.
A.REI.1
Page 4/10
C.
The commutative property must be used in the second step
to prove that the sides of the charge equation are equal.
D.
The division equality property must be used in the second
step to isolate and solve for the number of miles traveled.
7. Look at the equation.
Which statement best explains how to isolate x to the left side of the equation?
A. Divide
B. Add
by 2.
and
C. Add 2 to each side.
D. Subtract
from each side.
8.
Albert rewrote the equation
he use to rewrite the equation?
as
A. only the division property of equality
B. only the multiplication property of equality
A.REI.1
Page 5/10
Which properties did
C. the division and subtraction properties of equality
D. the multiplication and subtraction properties of equality
9. Part A. Solve the equation
property of equality that was used.
Justify each step by listing the
Part B. Mathew solved the equation
How is the justification for
each step in this equation different than the equation in part A?
Use words, numbers, and/or pictures to show your work.
10.
The first two steps Ria uses to solve the equation
below.
Step 1:
Step 2:
Which properties did she apply during these steps?
A. subtraction and multiplication properties of equality
B. addition and multiplication properties of equality
C. subtraction and division properties of equality
A.REI.1
Page 6/10
are shown
D. addition and division properties of equality
11. The steps used by Kate and Taylor to solve an equation
are shown below:
Kate :
Taylor :
Part A. List the properties of equality used in each step of the equation
on the lines above.
Part B. Did Katie and Taylor both solve the equation correctly? Explain
why or why not.
Use words, numbers, and/or pictures to show your work.
A.REI.1
Page 7/10
12. The steps used to solve an equation are shown below.
Which property can be used to justify Step 4?
A. Commutative Property of Addition
B. Subtraction Property of Equality
C. Addition Property of Equality
D. Inverse Operation Property
13. Which of these statements describes a correct method to solve the
equation shown below?
A. multiply by x on both sides, set the equation equal to zero, and then
solve by factoring
A.REI.1
Page 8/10
B. divide by x on both sides, set the equation equal to zero, and then
solve by factoring
C. cancel the x in the numerator and denominator, and then subtract 6
from both sides of the equation to solve
D. cancel the x in the numerator and denominator and then add 5 to
both sides of the equation to solve
14. Find all values of x that satisfy the equation shown below. Show your
work. Number each step of your work and state the property used.
15.
Kelly and Mike solved the equation
different methods, shown below.
Kelly:
A.REI.1
Page 9/10
using two
Mike:
Which statement best describes who solved the equation correctly?
A. Kelly and Mike both solved the equation correctly because both
methods used followed the properties of equality and, therefore, both
equations were balanced throughout the solving process.
B. Neither Kelly nor Mike solved the equation correctly because both
incorrectly used the properties of equality and, therefore, both
equations were not balanced throughout the solving process.
C. Only Kelly solved the equation correctly because Mike’s first step did
not follow a property of equality.
D. Only Mike solved the equation correctly because Kelly’s first step did
not follow a property of equality.
A.REI.1
Page 10/10