We have 30 miles of fencing which can be used to enclose a rectangular piece of grazing land along a straight portion of a river. No fence is required along the river. The grazing land will be subdivided into two sections by means of a fence parallel to the sides and perpendicular to the river.
Write a function that expresses the total area in terms of the width x of the side of the grazing area perpendicular to the straight river.

The area of the gazing land is square miles.

Step-by-step explanation:

Given that, 30 miles of fencing can be used to enclose a rectangular piece of grazing land along a straight piece of river.

Let the length of the rectangular piece of gazing which is along the river be y and the width of the  rectangular piece of gazing be x.

Along the river side, no fence is required.

Therefore total length of fence is = 2(x+y)-x

                                                        =2y+x

∴2y+x=30

⇒2y=30-x

The area of the rectangular piece of gazing is = Length×width

                                                                              =xy

                                                                              square miles.

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