Question

1.

What is the value of r in the equation 4r – 8 = 5r + 12? (4 points)


–20


–1


1


20






2.


Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y? (4 points)


5y = 2


5y = 10


11y = 2


11y = 10






3.


What is the value of n in the equation 3n + 2(n + 2) = 9n + 12? (4 points)


–4


–2


2


4






4.


How many solutions can be found for the equation –4x – 11 = 2(x – 3x) + 13? (4 points)


None


One


Two


Infinitely many






5.


The work of a student trying to solve the equation 2(2x – 3) = 6 + 2x + 4 is shown below:

Step 1: 2(2x – 3) = 6 + 2x + 4

Step 2: 4x – 3 = 10 + 2x

Step 3: 4x – 2x = 10 + 3

Step 4: 2x = 13

Step 5: x = 6.5

In which step did the student first make an error and what is the correct step? (4 points)


Step 2: 4x – 6 = 10 + 2x


Step 2: 4x – 3 = 2 + 2x


Step 3: 4x + 2x = 10 + 3


Step 3: 4x – 2x = 10 - 3

Answer 1

1. 20
Add -8 to both sides . Then add -5r .
R=20
2.5y=2
3. 2
4 .there's only one solution but that solution can be expressed differently.
0.66666 , 2/3
5.there are different errors , step 3 shows addiction then it shows subtraction , there is also a mistake (step2).

Answer 2

1. 4r-8=5r+12
4r-5r=12+8
-r=20(divide by -1)
r=-20

2. 8y+4=6+2y+1y
8y+4=6+3y
8y-3y=6-4
5y=2

3. 3n+2(n+2)=9n+12
3n+2n+4=9n+12
5n+4=9n+12
5n-9n=12-4
-4n=8(divide by -4)
n=-2

4. -4x-11=2(x-3x)+13
-4x-11=2x-6x+13
-4x-11=-4x+13
-4x+4x=13+11
∴there is no answer. it is undefined.

5.2(2x-3)=6+2x+4
4x-6=10+2x
4x-2x=10+6
2x=16
x=8