Which inequality will have a solid boundary line and a shaded region above its graph?

x − y ≥ 3

2x − 3y ≤ 3

3y − x < 2

2x + y < 7

B. 2x − 3y ≤ 3

Step-by-step explanation:

We are required to find the graph having solid boundary line.

When a graph have soled boundary line. Then, the inequality will have the equality sign in it.

That is, strict inequality can never have a solid boundary line.

So, option C and D are discarded.

Further, the graph must have shaded region above the graph.

Now, the region above the graph means that, the inequality must be of the form .

So, we have,

implies

So, option A is not correct.

But, implies

Thus, the inequality having solid boundary and graph above is .

step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal