2/3k-(k+1/4)=1/12(k+4)
To solve the equation 2/3k - (k + 1/4) = 1/12(k + 4), we will follow these steps:
Step 1: Distribute the fraction terms on both sides of the equation.
Multiply 1/12 with (k + 4):
(1/12) * (k + 4) = (1/12)k + (1/12)(4) = (1/12)k + 1/3
Now our equation becomes: 2/3k - (k + 1/4) = (1/12)k + 1/3
Step 2: Simplify the equation by removing parentheses.
Distribute the negative sign to (k + 1/4) by changing the sign of the terms inside the parentheses:
2/3k - k - 1/4 = (1/12)k + 1/3
Now our equation becomes: 2/3k - k - 1/4 = 1/12k + 1/3
Step 3: Combine like terms on both sides of the equation.
On the left side, combine the fractions with the same denominator:
2/3k - (3/3)k - 1/4 = 1/12k + 1/3
Simplify further:
(2/3 - 3/3)k - 1/4 = 1/12k + 1/3
-1/3k - 1/4 = 1/12k + 1/3
Step 4: Adjust the equation to have the same denominator.
Convert -1/3k to have the same denominator as 1/12k:
-4/12k - 1/4 = 1/12k + 1/3
Step 5: Combine the fractions on both sides of the equation.
Combine the fractions on the right side:
-4/12k - 1/4 = 1/12k + 4/12
Now our equation becomes: -4/12k - 1/4 = 1/12k + 4/12
Step 6: Simplify the equation further.
Combine the left side fractions:
(-4/12 - 3/12)k - 1/4 = 1/12k + 4/12
Simplify further:
(-7/12)k - 1/4 = 1/12k + 4/12
Step 7: Adjust the equation to have the same denominator.
Convert -7/12k to have the same denominator as 1/12k:
-7/12k - 3/12 = 1/12k + 4/12
Step 8: Combine the fractions on both sides.
Combine the fractions on the left side:
(-7/12 - 3/12)k - 3/12 = 1/12k + 4/12
Simplify further:
(-10/12)k - 3/12 = 1/12k + 4/12
Step 9: Combine like terms on both sides.
Combine the fractions on the left side:
(-10/12 - 1/12)k = 1/12k + 4/12 + 3/12
Simplify further:
(-11/12)k = 1/12k + 7/12
Step 10: Move all the terms with k to one side.
Subtract (1/12)k from both sides:
(-11/12)k - (1/12)k = 7/12
Simplify further:
(-11/12 - 1/12)k = 7/12
Step 11: Combine like terms on the left side.
(-12/12)k = 7/12
Simplify further:
-k = 7/12
Step 12: Solve for k.
Multiply both sides by -1:
(-1)(-k) = (-1)(7/12)
Simplify further:
k = -7/12
Therefore, the solution to the equation 2/3k - (k + 1/4) = 1/12(k + 4) is k = -7/12.