How do you solve #abs(4x-2) - 6=20#?

Question

Julia Adams · Accepted Answer

Solve |4x - 2| - 6 = 20

Separate solving into 2 parts: a. (4x - 2) = 26 -> 4x = 28 -> x = 7 b. - (4x - 2) = 26 -> -4x = 24 -> x = - 6

Kennedy Adams · Answer

undefined To solve the equation |4x - 2| - 6 = 20:

1. Add 6 to both sides of the equation to isolate the absolute value term:
   |4x - 2| = 20 + 6
   |4x - 2| = 26

2. Now, split the equation into two cases:
   Case 1: 4x - 2 is positive
   Case 2: 4x - 2 is negative

3. For Case 1 (4x - 2 is positive):
   4x - 2 = 26
   Solve for x:
   4x = 26 + 2
   4x = 28
   x = 28/4
   x = 7

4. For Case 2 (4x - 2 is negative):
   -(4x - 2) = 26
   Solve for x:
   -4x + 2 = 26
   -4x = 26 - 2
   -4x = 24
   x = 24/(-4)
   x = -6

5. Therefore, the solutions to the equation are x = 7 and x = -6.

Kennedy Adams · Answer

undefined To solve the equation $ |4x - 2| - 6 = 20 $, follow these steps:

1. Add 6 to both sides of the equation:
   $ |4x - 2| = 20 + 6 = 26 $

2. Since the absolute value of any real number is always non-negative, this means that $ |4x - 2| $ must be equal to either 26 or -26:
   $ 4x - 2 = 26 $ or $ 4x - 2 = -26 $

3. Solve each equation separately:
   For $ 4x - 2 = 26 $:
   $ 4x = 26 + 2 $
   $ 4x = 28 $
   $ x = \frac{28}{4} $
   $ x = 7 $

For $ 4x - 2 = -26 $:
   $ 4x = -26 + 2 $
   $ 4x = -24 $
   $ x = \frac{-24}{4} $
   $ x = -6 $

So, the solutions to the equation $ |4x - 2| - 6 = 20 $ are $ x = 7 $ and $ x = -6 $.