To solve the equation, we need to isolate the absolute value term.

First, we subtract 7 from both sides of the equation:

2|3x - 1| = 10

Next, we divide both sides of the equation by 2:

|3x - 1| = 5

Now, we have two cases to consider:

Case 1: 3x - 1 is positive

If 3x - 1 is positive, then the absolute value of 3x - 1 is equal to 3x - 1.

So, we can rewrite the equation as:

3x - 1 = 5

Adding 1 to both sides:

3x = 6

Dividing both sides by 3:

x = 2

Case 2: 3x - 1 is negative

If 3x - 1 is negative, then the absolute value of 3x - 1 is equal to -(3x - 1), which is equal to -3x + 1.

So, we can rewrite the equation as:

-3x + 1 = 5

Subtracting 1 from both sides:

-3x = 4

Dividing both sides by -3:

x = -4/3

Therefore, the solutions to the equation are x = 2 and x = -4/3.