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

User Belzebub
by
7.8k points

2 Answers

6 votes

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

User Usmanwalana
by
8.4k points
4 votes

Answer:

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

User Vladimir Dzhuvinov
by
9.3k points

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