Question

Which steps can be taken to translate the phrase “the height of a tree is increased by seven inches” into an algebraic expression? Check all that apply. 

Replace “the height of a tree” with a variable, x.

Replace “seven inches” with a variable, x.

Replace “increased by” with an addition symbol.

Replace “seven inches” with 7.

Replace “increased by” with a multiplication symbol.

Replace “the height of a tree” with 7.

Write the expression .

Write the expression .

Comments

2. Substitute  and  to determine if the two expressions are equivalent.

                        

Which statements are true? Check all that apply. 

The value of both expressions when  is 33.

The value of both expressions when  is 23.

The value of both expressions when  is 41.

The value of both expressions when  is 51.

The two expressions are equivalent.

The two expressions are not equivalent.

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Juan used algebraic properties to make an equivalent expression. He listed the properties in the order that he used them. 
 

 

Step	Property Used
1	Associative
2	Distributive
3	Addition

Which steps match the properties used?

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Part of number 3.

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Fiona doubled the original amount in her savings account, s. Which expression represents her new balance and what is that new balance if ?

; when  the new balance in Fiona’s savings account is $80.

; when  the new balance in Fiona’s savings account is $320.

; when  the new balance in Fiona’s savings account is $320.

; when  the new balance in Fiona’s savings account is $80. 4. 

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5. Dan’s new appliance arrived in a cardboard box in the shape of cube. What is the surface area of the cardboard box?

Use the formula , where SA is the surface area of the cube and s is the length of each side.

18 

36 

54 

324 

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6. Which expression is equivalent to ?

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7. Which expression correctly represents “ten times the difference of a number and six”?

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8. Misha’s family bought a large cattle farm. The number of acres of the cattle farm is the cube of the acres they used to own plus 10 acres. If a represents the number of acres the family used to own, which expression represents the number of acres they own now?

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9. Jillian was asked to translate the expression  into words. She wrote “a number increased by nine.” Which best describes the accuracy of Jillian’s answer?

It is incorrect. The variable would come first in the expression “a number” (n) “increased by” (+) “nine” (9).

It is incorrect. The phrase “increased by” refers to the inequality symbol “greater than” (>), not addition.

It is correct. A number increased by nine () is the same as nine increased by a number ().

It is incorrect. A number increased by nine refers to a multiplication expression ().

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10. Which scenario could be represented by the algebraic expression ?

Ariel wants to find the difference of a number and 13.

Ariel wants to find the product of 13 and a number.

Ariel wants to find the sum of a number and 13.

Ariel wants to find the difference of 13 and a number.

Answer 1

1. 1 3 4 7
2. 1 4 5
3. 3
4. 3
5. 3
6. 2
7. 1
8. 3
9. 3
10. 1
11.  

Answer 2

s t f u okay