Solve. -9(4-k)/12 = 9(k+1)/8
divide both sides by -9
(4-k)/12 = -(k+1)/8
cross-multiply
8(4-k) = -12(k+1)
32 - 8k = -12k - 12
4k = -44
k = -11
8(4-k)=-12(k 1)
24-8k=-12k-12
-8k 12k=-12-24
4k=-36
K=-9
To solve the equation, we need to simplify both sides and then isolate the variable. Let's start step by step.
Given equation: -9(4 - k)/12 = 9(k + 1)/8
1. Distribute the -9 on the left side:
-9 * 4 = -36
-9 * -k = 9k
So, the left side becomes: -36 + 9k/12 = 9(k + 1)/8
2. Simplify the left side:
-36 + 9k/12 can be further simplified by dividing both terms by the greatest common divisor (GCD) between 36 and 12, which is 12:
-3 + 3k/4 = 9(k + 1)/8
3. Multiply through by the common denominator:
To get rid of the denominators, we can multiply both sides by 8 and 4 to eliminate fractions.
Multiply the left side by 8:
8 * (-3 + 3k/4) = 8 * 9(k + 1)/8
-24 + 6k = 9(k + 1)
4. Distribute the 9 on the right side:
-24 + 6k = 9k + 9
5. Move all terms involving 'k' to one side and the constant terms to the other side:
Rearranging the equation:
6k - 9k = 9 - (-24)
-3k = 33
6. Divide both sides by -3 to solve for 'k':
k = 33 / -3
k = -11
The solution to the equation is k = -11.