Question

(ILL GIVE YOU 100 POINTS!!)

The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?

a Step 2; 8x − 4 = 2(6 + x + 6)

b Step 2; 8x − 16 = 16 + 2x

c Step 3; 6x − 2x = 16 − 8

d Step 3; 6x + 2x = 16 + 8

Answer 1

Here, The work of a student to solve the equation :

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

The steps for calculating the value of x are :

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

Step 2:
`6x - 8 = 16 + 2x`

Step 3:
`6x - 2x = 16 + 8`

Step 4:
`4x = 24`

Step 5:
`x = 6`

Step 2 is incorrect, as the student instead of multiplying, adds the number as:

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

Here, the correct step is:

`\boxed{\bold{8x - 16 = 16 + 2x}}`

`6 x = 32`

`x = 5.33`

So, the error is in STEP 2 and the correct option is (B).

Answer 2

step 2 is wrong

Explanation:

• 4 multiply by 2x = 8x
• 4 multiply by -4 = -16

CORRECT STEP

• 4(2x - 4) = 8 + 2x + 8
• 8x - 16 = 8 + 2x + 8
• 8x - 16 = 2x + 16
• 6x = 32
• x = 32/6 = 5 ( approximately )