Question

How do you solve `3/2y-y=4+.5y`?

Answer 1

See a solution process below:

Explanation:

First, convert `3/2` to:

`3/2 = (2 + 1)/2 = 2/2 + 1/2 = 1 + 1/2 = 1 + 0.5 = 1.5`

We can rewrite the problem as:

`1.5y - y = 4 + 0.5y`

Next, we can combine like terms on the left side of the equation:

`1.5y - 1y = 4 + 0.5y`

`(1.5 - 1)y = 4 + 0.5y`

`0.5y = 4 + 0.5y`

Now, we can subtract `color(red)(0.5y)` from each side of the equation to show there is no solution:

`0.5y - color(red)(0.5y) = 4 + 0.5y - color(red)(0.5y)`

`0 = 4 + 0`

`0 != 4`

Because `0` is obviously not equal to `4` there is no solution for this problem

Or, the solution is the null or empty set: `{O/}`

Answer 2

No solutions

Explanation:

`3/2` is the same thing as `1.5`. With this in mind, we can rewrite our equation as

`1.5y-y=4+0.5y`

We have two `y` terms on the left, so we can simplify them to get

`0.5y=4+0.5y`

Something already looks suspicious...let's subtract `0.5y` from both sides to get

`0=4`

This is obviously not true, which means no value of `y` satisfies this equation.

Hope this helps!