5y/12-y-3/6=2y-1/2
To solve the equation 5y/12 - y - 3/6 = 2y - 1/2, we need to simplify and rearrange the equation to isolate the variable y.
Step 1: Simplify the equation by finding a common denominator for the fractions. In this case, we can use 12 as the common denominator.
5y/12 - y - 3/6 = 2y - 1/2 becomes:
5y/12 - 12y/12 - 6/12 = 2y - 1/2
Now we have:
(5y - 12y - 6)/12 = 2y - 1/2
Step 2: Combine like terms on both sides of the equation.
(-7y - 6)/12 = 2y - 1/2
Step 3: Eliminate the denominators by multiplying both sides of the equation by 12 (the least common multiple of the denominators).
12 * (-7y - 6)/12 = 12 * (2y - 1/2)
On the left side, the 12s cancel out, leaving:
-7y - 6 = 24y - 6
Step 4: Simplify the equation by moving all terms with y to one side and all constants to the other side.
Add 7y to both sides:
-7y + 7y - 6 = 24y + 7y - 6
Simplifying further:
-6 = 31y - 6
Next, add 6 to both sides:
-6 + 6 = 31y - 6 + 6
Simplifying further:
0 = 31y
Step 5: Solve for y.
Since anything multiplied by 0 is 0, this equation tells us that y can be any value. Therefore, the solution to the equation 5y/12 - y - 3/6 = 2y - 1/2 is y = any real number.