Solve the following equation for x. 6 − |4x − 2/3| = 4 x = { }

To solve the equation (6 – |4x – frac{2}{3}| = 4), we can start by isolating the absolute value.

1. Subtract 6 from both sides:

[

-|4x – frac{2}{3}| = -2

]

2. Multiply both sides by -1:

[

|4x – frac{2}{3}| = 2

]

Now we need to consider the two cases for the absolute value.

Case 1:

[

4x – frac{2}{3} = 2

]

Add (frac{2}{3}) to both sides:

[

4x = 2 + frac{2}{3}

]

Convert 2 to a fraction:

[

4x = frac{6}{3} + frac{2}{3} = frac{8}{3}

]

Now, divide by 4:

[

x = frac{8}{3} div 4 = frac{8}{12} = frac{2}{3}

]

Case 2:

[

4x – frac{2}{3} = -2

]

Again, add (frac{2}{3}) to both sides:

[

4x = -2 + frac{2}{3}

]

Convert