Question

HELP!!!

1. What is the value of x in the equation −x = 2 − 3x + 6?

8
4
−4
−8

2. The work of a student to solve the equation 2(3x − 4) = 8 + 2x + 4 is shown below:

Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x
Step 3: 5x − 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6

In which step did the student first make an error and what is the correct step?

Step 2; 6x − 6 = 2(6 + x + 2)
Step 2; 6x − 8 = 12 + 2x
Step 3; 5x − 2x = 12 − 6
Step 3; 5x + 2x = 12 + 6

3. The steps below show the incomplete solution to find the value of m for the equation 4m − 2m + 4 = −1 + 13:

Step 1: 4m − 2m + 4 = −1 + 13
Step 2: 4m − 2m + 4 = 12
Step 3: 2m + 4 = 12

Which of these is most likely the next step?

2m = 3
2m = 8
2m = 16
2m = 18

Answer 1

1.
-x = 2 - 3x + 6
-x + 3x = 8
2x = 8
x = 8/2
x = 4

2.
Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x ← wrong
The correct step: Step 2: 6x − 8 = 12 + 2x

3.
The next step is 2m = 8

Answer 2

1. The correct option is 2.

2. The correct option is 2.

3. The correct option is 2.

Explanation:

Part 1.

The given equation is

`-x=2-3x+6`

Add 3x on both sides.

`-x+3x=2-3x+6+3x`

Combine like terms.

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

`2x=8`

Divide both sides by 2.

`(2x)/(2)=(8)/(2)`

`x=4`

The value of x is 4. Therefore option 2 is correct.

Part 2.

The given equation is

`2(3x-4) = 8 + 2x + 4`

Step 1:
`2(3x-4) = 8 + 2x + 4`

Step 2:
`6x-8 = 12 + 2x`

Step 3:
`6x-2x = 12 + 8`

Step 4:
`4x = 20`

Step 5:
`x = 5`

Student make his first mistake in step 2 and the correct step is 6x-8 = 12 + 2x. Therefore the correct option is 2.

Part 3.

The given equation is

`4m-2m + 4 = -1 + 13`

Step 1:
`4m-2m + 4 = -1 + 13`

Step 2:
`4m-2m + 4 = 12`

Step 3:
`2m + 4 = 12`

Step 4: Subtract 4 from both sides.

`2m= 12-4`

`2m= 8`

The next step is 2m= 8. Therefore the correct option is 2.