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