R.R1.P1 Regents Review #1 Identifying properties/Solving Linear

• addition property of equality

• commutative property of addition

• multiplication property of equality

• distributive property of multiplication over addition

• identity property of multiplication

• multiplication property of equality

• commutative property of multiplication

• distributive property of multiplication over subtraction

• I and III

• I and IV

• II and III

• II and IV

The solution to 3(x − 8) + 4x = 8x + 4 is

Mathematical Equivalence

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A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking.

Which linear equation can be used to find x, the additional hourly parking rate?

Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?

Hannah went to the school store to buy supplies and spent $16. She bought four more pencils than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each. If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought. Use your equation to determine algebraically how many pens Hannah bought

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Answer explanation

1.25x + 0.55(x + 4) + 0.75(x − 2) = 16

1.25x + 0.55x + 2.2 + 0.75x − 1.5 = 16

2.55x + 0.7 = 16

2.55x = 15.3

x = 6