Question

1. Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?

A.8,000 + 24x
B.8,000 − 24x
C.8,000 + 2x
D.8,000 − 2x

2. Avi and Sergi are saving money to buy a game system. Avi has $2 more than double the amount of money Sergi has. Together, they have $40. Write an equation to determine how much money Sergi and Avi have together.

A.x + 2x + 2 = 40
B.2x + 2 = 40
C.x + 2x − 2 = 40
D.2x − 2 = 40

Isabella solved the following equation:

4x − 2x + 8 = 6(x + 4)


Step Work Justification
1 4x − 2x + 8 = 6x + 24 Distributive Property
2 2x + 8 = 6x + 24 Combine like terms
3 −4x + 8 = 24 Addition Property of Equality
4 −4x = 16 Subtraction Property of Equality
5 x = −4 Division Property of Equality

Which step has an incorrect justification?
A.Step 1
B.Step 2
C.Step 3
D.Step 4

Answer 1

1. C. 8000 - 24x; 2 A. x + 2x + 2 = 40; 3. C. Step 3

Explanation

1. Desmond

`\begin{array}{rcl}\text{Value of car two years ago} & = & 8000\\\\\text{Less depreciation = 24 mo} *\frac{x}{\text{1 mo}} & = & -24 x\\\\\text{Current value} & = & \mathbf{8000 - 24x}\\\end{array}`

2. Avi and Sergi

`\begin{array}{rcl}\text{Sergi's money} & = & x\\\text{Double Sergi's money} & = & 2x\\\text{Avi's money} & = & 2x + 2\\\text{Avi's money + Sergi's money} & = & x + 2x + 2\\\text{Avi's money + Sergi's money} & = & 40\\x + 2x + 2 & = & 40\\\end{array}`

3. Isabella

`\begin{array}{crl} \textbf{Step} & \textbf{Work} & \textbf{Justification} \\ & 4x - 2x + 8 = 6(x + 4) & \\ 1 & 4x - 2x + 8 = 6x + 24 & \text{Distributive Property} \\ 2 & 2x + 8 = 6x + 24 & \text{Combine like terms} \\ 3 & -4x + 8 = 24 & \textbf{Subtraction Property of Equality}\\ 4 & -4x = 16 & \text{Subtraction Property of Equality} \\ 5 & x = -4 & \text{Division Property of Equality} \\ \end{array}`

Step 3 has the incorrect justification. Isabella subtracted 6x from each side, so she should have used the Subtraction Property of Equality