Final answer:
To solve the equation 1/6y + 5/2y = -5, first find a common denominator for the y terms, then combine the y terms and simplify. Finally, divide both sides of the equation by the coefficient of y to solve for y.
Step-by-step explanation:
To solve the equation 1/6y + 5/2y = -5, we need to combine the y terms on one side of the equation and the -5 on the other side. First, find a common denominator for the y terms, which is 6. So, the equation becomes 1/6 * y + 5/2 * y = -5. Multiply each term by its denominator and simplify:
(1/6) * y + (5/2) * y = -5
1/6 * y + 15/6 * y = -5
Now, combine the y terms:
(1/6 + 15/6) * y = -5
(16/6) * y = -5
Distribute the 16/6 to y:
(16/6) * y = -5
(8/3) * y = -5
Now, divide both sides of the equation by 8/3 to solve for y:
y = (-5) / (8/3)
Simplify the division:
y = (-5) * (3/8)
y = -15/8