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5 votes
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

2 Answers

5 votes
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
User Mahesh Keshvala
by
8.8k points
6 votes

Answer:

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.

User Marek Sebera
by
7.9k points

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