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Question

Solve for k.
20 = 2|2k|
Write your answers as integers or as proper or improper fractions in simplest form
k =
or
k =

Answer 1

To solve for k, we need to isolate the absolute value expression.

First, divide both sides of the equation by 2:
20/2 = |2k|
10 = |2k|

Next, remove the absolute value by considering both cases:
Case 1: 2k > 0
For this case, we can remove the absolute value signs:
10 = 2k

Now, divide both sides by 2:
10/2 = k
5 = k

Case 2: 2k < 0
For this case, we need to make the absolute value expression negative by multiplying it by -1:
10 = -2k

Divide both sides by -2:
10/(-2) = k
-5 = k

Therefore, the solutions for k are:
k = 5 or k = -5.