# Which ordered pair is in the solution set of 0.5x-2y>=3?

May 23, 2017

Any ordered pair $\left(x , y\right)$ that satisfies $x \ge 6 + 4 y$
Or, in set notation, $S o l u t i o n = \left\{\left(x , y\right) | x \ge 6 + 4 y\right\}$

#### Explanation:

Now, there is a little problem here - it is that you never specified which ordered pair needs to be evaluated to satisfy the condition $0.5 x - 2 y \ge 3$ Allow me to explain.

Below is a graph of the inequality of your question:
graph{0.5x-2y>=3 [-10, 10, -5, 5]}
To answer which point is in the solution set, well the answer is that any point that is on or within the shaded area is part of the solution set.

Let's reorganize the initial inequality:
$0.5 x - 2 y \ge 3$
$0.5 x \ge 3 + 2 y$
$x \ge 6 + 4 y$

Now, let us suppose we have a coordinate pair $\left(6 , 0\right)$ and we would like to evaluate whether it is in the solution set.
To do that, we substitute $x = 6$ and $y = 0$ into $x \ge 6 + 4 y$.
We get $6 \ge 6$ which is true. So, $\left(6 , 0\right)$ is part of the solution set.

As stated in the answer above, we can notate the set of all points named $S$ as:
$S = \left\{\left(x , y\right) | x \ge 6 + 4 y\right\}$