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

Mathematics

2 answers:

bulgar [2K]1 year ago

8 0

Answer:

x=6 and -14/3

Step-by-step 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

umka21 [38]1 year ago

7 0

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

$\frac{2(|3x-2|)}{2} = \frac{20}{2}$

$=|3x-2|=10$

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.

<h2>Possibility 1</h2>

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

<h2>Possibility 2</h2>

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

Thus,

The answer is: x = 4 or x = $\frac{-8}{3}$

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

-Garebear

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