Solve for k.
5k/3 – 3 = 1/3 + 2k
k = ___
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To solve for ( k ) in the equation
[
frac{5k}{3} – 3 = frac{1}{3} + 2k,
]
let’s follow these steps:
1. Eliminate Fractions: Multiply the entire equation by 3 to clear the denominators:
[
3 left( frac{5k}{3} right) – 3 cdot 3 = 3 left( frac{1}{3} + 2k right)
]
This simplifies to:
[
5k – 9 = 1 + 6k
]
2. Rearrange the Equation: Move all terms involving ( k ) to one side and constant terms to the other side:
[
5k – 6k = 1 + 9
]
This simplifies to:
[
-k = 10
]
3. Solve for ( k ): Multiply both sides by -1:
[
k = -10
]
Thus, the solution is
[
k = -10.
]
Feel free to ask if you have more questions or if you need further explanations!