Question

The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below:

Step 1: 3(2x − 4) = 8 + 2x + 6
Step 2: 5x − 7 = 14 + 2x
Step 3: 5x − 2x = 14 + 7
Step 4: 3x = 21
Step 5: x = 7

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

Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7

Answer 1

Ok so, in PEMDAS, you do what first?

Answer 2

Im assuming Imma have to guide you through this....

Answer 3

So, in step one, you would distribute the 3 to 2x and -4.

Answer 4

Was step one done correctly?

Answer 5

Ok... think about it this way:
3 x 2 = 6 and -4 x 3 =-12

Answer 6

Yes. Step one was done correctly.

Answer 7

Ok, so, if we take a look, if it's distributed properly, step 2 would look like this:
6x-12 = 8+2x+6
Then when you combine like terms, it would look like this:
6x-12=2x+14
Does step 2 look correct?

Answer 8

Step 2 is correct when we correctly solve Step 1.

Answer 9

But is the person's step 2 correct in the problem?

Answer 10

No.

Answer 11

We have to use the Order of Operations, aka PEMDAS.

Answer 12

In the equation 3(2x − 4) = 8 + 2x + 6, the person messed up by using the distributive property.

Answer 13

The first option is "Step 2; 6x − 12 = 14 + 2x", which is correct in this case.

Answer 14

That's it!

Answer 15

Teamwork makes the dream work!

Answer 16

*help

Answer 17

Have a blessed day!