Question

1/2-1 3/5y=4 1/2-3y

Answer 1

1/2-1 3/5y= 4 1/2-3y
-1 3/5y+3y= 4 1/2-1/2
1 2/5y= 4
y=4:1 2/5
y=4*5/7
y=20/7
y=2 6/7

Answer 2

To solve for the variable "y" in the equation:

1/2 - (1 3/5)y = 4 1/2 - 3y

You can start by simplifying both sides of the equation step by step.

First, let's work on the left side of the equation:

1/2 - (1 3/5)y

To subtract the mixed number (1 3/5) from 1/2, you need to find a common denominator, which is 10:

1/2 - (8/5)y

Now, to get rid of the fraction on the left side, multiply both sides of the equation by 10:

10 * (1/2) - 10 * (8/5)y = 10 * (4 1/2) - 10 * (3y)

5 - (8/5)y = 45 - 30y

Now, let's work on the right side of the equation:

4 1/2 - 3y

To express 4 1/2 as an improper fraction:

4 1/2 = 9/2

So, the equation becomes:

(9/2) - 3y

Now, let's put the equation back together:

5 - (8/5)y = 45 - 30y

Now, you can simplify the equation by moving all the terms with "y" to one side of the equation and the constants to the other side:

(8/5)y - 30y = 45 - 5

To combine the "y" terms, find a common denominator, which is 5:

(8/5)y - (150/5)y = 40

Now, subtract the fractions:

(8/5 - 150/5)y = 40

(-142/5)y = 40

Now, solve for "y" by dividing both sides by (-142/5):

y = (40) / (-142/5)

To divide by a fraction, you can multiply by its reciprocal:

y = 40 * (-5/142)

Now, simplify the right side:

y = -200/142

You can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 2:

y = (-100/71)

So, the solution to the equation is:

y = -100/71