solve -[-(-k)]-(-2)(-2+k)=-k-(4k+3)
"clean up" all those negative signs first.
-[-(-k)]-(-2)(-2+k)=-k-(4k+3)
-k + 2(-2+k) = -k - 4k - 3
-k - 4 + 2k = -5k - 3
6k = 1
k = 1/6
To solve the equation -[-(-k)] - (-2)(-2+k) = -k - (4k + 3), we will first simplify both sides of the equation and then solve for the variable 'k'.
Let's start with the left side of the equation:
-[-(-k)] - (-2)(-2+k)
To simplify the expression -[-(-k)], we need to remove the negative signs. Since there are two sets of negative signs here, the expression becomes positive:
[-(-k)] = k
Now let's simplify the expression (-2)(-2+k):
(-2)(-2+k) = (-2)(-2) + (-2)(k)
= 4 - 2k
Now our equation becomes:
k - 4 + 4 - 2k = -k - (4k + 3)
Simplifying further:
- k - 2k = -k - (4k + 3)
- 3k = -k - 4k - 3
- 3k = -5k - 3
Next, let's simplify the right side of the equation:
-5k - 3 can be rewritten as -5k + (-3) to avoid confusion with subtraction.
Now our equation becomes:
-3k = -5k + (-3)
To solve for 'k', let's isolate the variable 'k' on one side of the equation. We will move the terms involving 'k' to the left side, and the constant terms to the right side:
-3k + 5k = -3
2k = -3
Finally, let's solve for 'k' by dividing both sides of the equation by 2:
2k/2 = -3/2
k = -3/2
Therefore, the solution to the equation -[-(-k)] - (-2)(-2+k) = -k - (4k + 3) is k = -3/2.