Question

The difference between two numbers is greater than
2
. David created, solved, and graphed an inequality to represent the possible values of the numbers but made an error. David wrote the inequality
x
−
y
>
2
to represent the possible values of the numbers where
x
is the larger number and
y
is the smaller number. He then solved the inequality for
y
and graphed the inequality.

x
−
y
>
2

−
y
>
−
x
+
2

y
>
x
−
2



image

Which of the following BEST evaluates the work shown by David?

A.
Solution: David created an incorrect inequality for the situation and incorrectly solved it for
y
.

Reasoning: The inequality would be
y
−
x
>
2
which when solved for
y
would be
y
>
x
+
2
. However, this inequality will have the same graph as the inequality David graphed.

B.
Solution: David created a correct inequality for the situation but incorrectly solved it for
y
.

Reasoning:The solution would be
y
<
x
−
2
. However, this inequality will have the same graph as the inequality David graphed.

C.
Solution: David created a correct inequality for the situation but incorrectly solved it for
y
.

Reasoning:The solution would be
y
<
x
−
2
. This also means David’s graph is shaded on the wrong side of the boundary line for the situation.

D.
Solution: David created a correct inequality for the situation and correctly solved it for
y
.

Reasoning:David shaded the wrong side of the boundary line when graphing the solution set.

Answer 1

C

David started with the correct inequality x − y > 2, but made an algebra error when isolating y:

x − y > 2
−y > 2 − x
multiply both sides by −1 (reverse inequality):
y < x − 2.

So the correct solution is y < x − 2, and David’s graph (y > x − 2) is shaded on the wrong side of the boundary.