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

Jul 16, 2018

See a solution process below:

#### Explanation:

First, convert $\frac{3}{2}$ to:

$\frac{3}{2} = \frac{2 + 1}{2} = \frac{2}{2} + \frac{1}{2} = 1 + \frac{1}{2} = 1 + 0.5 = 1.5$

We can rewrite the problem as:

$1.5 y - y = 4 + 0.5 y$

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

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

$\left(1.5 - 1\right) y = 4 + 0.5 y$

$0.5 y = 4 + 0.5 y$

Now, we can subtract $\textcolor{red}{0.5 y}$ from each side of the equation to show there is no solution:

$0.5 y - \textcolor{red}{0.5 y} = 4 + 0.5 y - \textcolor{red}{0.5 y}$

$0 = 4 + 0$

$0 \ne 4$

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

Or, the solution is the null or empty set: $\left\{\emptyset\right\}$

Jul 16, 2018

No solutions

#### Explanation:

$\frac{3}{2}$ is the same thing as $1.5$. With this in mind, we can rewrite our equation as

$1.5 y - y = 4 + 0.5 y$

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

$0.5 y = 4 + 0.5 y$

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

$0 = 4$

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

Hope this helps!