Question

Which point lies in the solution set of the inequality 1/2(x+2)+3y<8?

Answer 1

Note: Options are missing. So, the general solution of the given inequality is shown below.

Given:

The inequality is:

$\dfrac{1}{2}(x+2)+3y$

To find:

The point lies in the solution set of the given inequality.

Solution:

We have,

$\dfrac{1}{2}(x+2)+3y$

It can be written as:

$\dfrac{1}{2}(x)+\dfrac{1}{2}(2)+3y$

$\dfrac{1}{2}x+1+3y$

$\dfrac{1}{2}x+3y$

$\dfrac{1}{2}x+3y$

All the points that satisfy the above inequality are in the solution set of the given inequality.

For example (0,0).

$\dfrac{1}{2}(0)+3(0)$

$0$

This statement is true. It means (0,0) is in the solution set.

For example (0,3).

$\dfrac{1}{2}(0)+3(3)$

$9$

This statement is false. It means (0,3) is not in the solution set.

The graph of the inequality $\dfrac{1}{2}x+3y$ is shown below.

All the points in the shaded region are in the solution set but the points on the boundary line are not in the solution set.