Question

Solve the following equation:
2|3x - 2| -4 = 16

Answer 1

Hi there,

I hope you and your family are staying safe and healthy!

Let's solve the equation

`2|3x -2| -4 = 16`

The first step here is to add 4 on both sides

`2(|3x-2|)-4+4=16+4\\=2(|3x-2|)=20`

We're not done yet! So now we need to divide both sides by 2

`(2(|3x-2|))/(2) = (20)/(2)`

`=|3x-2|=10`

Now we need to solve for the absolute value

We know either
`3x - 2 = 10` or
`3x-2=-10`

Therefore, there are two possibilities here.

Possibility 1

`3x - 2 = 10 \\3x = 10 + 2\\3x = 12\\x = 12/3\\x = 4`

Possibility 2

`3x - 2 = -10\\3x = -10 + 2 \\3x = -8\\x = -8/3\\`

Thus,

The answer is: x = 4 or x =
`(-8)/(3)`

Happy to help! I wish you all the best this semester :)

-Garebear

Answer 2

x=6 and -14/3

Explanation:

Divide 2:

|3x - 2|-4 = 16

Plus 4: |3x - 2| = 16

So 3x - 2=16 and -3x + 2=16

3x - 2=16: x=6

-3x + 2=16: x=-14/3