Question

Graph the inequality 30 + 5y ≥ 4x . State 2 points in the region of solution and 2 points outside the region of solution.

Answer 1

Answer:

(0,-6) and (-2, -2) for region of solution

(10,10) and (11,11) for outside the region

Step-by-step explanation:

Hello :)

To answer this problem, we first need to find a way to graph this inequality. To do this, let's make it equal to y and pretend it's not an inequality for a second (sometimes math makes things complicated but it's truly not as hard as you think.)

30+5y$\geq$4x    Let's get the 30 out of here, get it to the other side by subtracting both sides by 30.

-30       -30

5y$\geq$4x-30    Isolate the y variable by dividing everything by five.

$y\geq \frac{4x}{5} -6$    is the equation simplified (-30 divided by five is -6).

Let's graph this. From this graph, we can clearly see that the y-intercept is (0,-6) and the slope is 4/5.

The graph is attached.

Now, since it's an inequality, only one side of the graph is supposed to fit the equation over the other side. Let's use a test point from the left and right side of the line. This will help us determine which part of the line follows the inequality.

Test point for the left: (0,-6)

Let's input it into the equation.

-6$\geq$$\frac{4(0)}{5}$-6

-6$\geq$-6            Since the inequality says greater than OR EQUAL to, this point satisfies the inequality, which means that the left side is the shaded part.

Test point for the right: (8, -2)

Let's input it into the equation.

$-2\geq \frac{4(8)}{5} -6$

-2$\geq$6.4-6

-2$\geq$0.4       This is not a true inequality, -2 is not greater than or equal to 0.4 so the right side is not shaded.

To find the points of solution outside and inside, we just need to pick two points from each that doesn't and does satisfy the equation.

I chose, in the shaded side, the region of solution, as (0,-6) and (-2, -2) and in the unshaded side, outside the region of solution, as (10,10) and (11,11)