Final answer:
To solve the given equation for x in terms of k, we distribute, combine like terms, and rearrange the equation to isolate x, resulting in the solution x = -0.5k.
Step-by-step explanation:
To solve for x in the equation x - 0.5(k - 3x) = 1.5x - k, we need to rearrange the terms to isolate x. Start by distributing the -0.5 across the parentheses:
x - 0.5k + 1.5x = 1.5x - k
Next, combine like terms on both sides of the equation:
2.5x - 0.5k = 1.5x - k
Now, subtract 1.5x from both sides to get all the x terms on one side:
x - 0.5k = -k
Then, add 0.5k to both sides to get all the k terms on the other side:
x = -k + 0.5k
Finally, simplify to find x:
x = -0.5k
Therefore, the solution for x in terms of k is x = -0.5k.