Show:
Expressions
Balancing (7th)
Balancing (8th)
Number of Solutions
Error Analysis
100

Simplify:

5x+3x−2+7


8x+5

100

−2x+5=9

x=−2

100

2x+6=x+9

x=3

100

One, No, or Infinite Solutions. 

Show work/explain to group for full credit.

x+5=12

One Solution

x=7

100

1) Explain the error

2) What is the correct answer

A student says:
3x + 2x = 5x^2

They multiplied instead of combining like terms
Correct answer: 5x

200

Simplify:

6(x−1)−2x

4x−6

200

3x−8=−2

x=2

200

−3x+6=x+4

x=1/2 or 1.5

200

One, No, or Infinite Solutions. 

Show work/explain to group for full credit.

2(x+3)=2x+9

No Solution

200

1) Explain the error

2) What is the correct answer

A student expands:
2(x+4)=2x+4

They forgot to distribute to both terms
Correct: 2x+8

300

Factor:

10x+20+5x

15x+20 = 5(3x+4)

300

(x/-4)+3=−1

x=16

300

4(x+1)=2(x+5)

x=3

300

One, No, or Infinite Solutions. 

Show work/explain to group for full credit.

4(x+2)=4x+8

Infinite Solutions

300

1) Explain the error

2) What is the correct answer

Solve attempt:
2(x+5)=12
x=3.5

Student forgot to expand to the 5
Correct: x=1

400

Simplify:

−3(x+4)+2(x+1)

−x−10 

400

−5x−7=18

x=−5

400

−2(x+5)=3(x−1)

x=-7/5 or -1and2/5 or -1.4

400

One, No, or Infinite Solutions. 

Show work/explain to group for full credit.

3x-5=2x+1

One Solution

x=6

400

1) Explain the error

2) What is the correct answer

A student solves:
2x+3=2x+7 → one solution: x=4

Variables cancel so 3=7

No solution

500

A rectangle has length x+3 and width 2.
Write and simplify an expression for the perimeter.

2x+10

500

Show your work both ways, dividing and distributing:

3(-x+4)=9

x=1

500

3(x−4)=−2(x+5)

x=2/5 or 0.4

500

One, No, or Infinite Solutions. 

Show work/explain to group for full credit.

-2(x+3)=-2x-6

Infinite Solutions

500

1) Explain the error

2) What is the correct answer

Solve for x. 
Find the value for x when dealing with a rectangle. The perimeter is 2x. The length of the rectangle is 2x-9 and the width of the rectangle is x+1. 

Student answer: x= 8

Student forgot to double the width and length. 

Correct answer x = 4