Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?
\n","rationale_html":"Choice B is correct. Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality gives
. So the given system of inequalities is equivalent to the system of inequalities
and
, which can be rewritten as
. Using the transitive property of inequalities, it follows that
.
Choice A is incorrect because there are points with a y-coordinate less than 6 that satisfy the given system of inequalities. For example, satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality
for x, then replacing x with y. Choice D is incorrect because this inequality allows y-values that are not the y-coordinate of any point that satisfies both inequalities. For example,
is contained in the set
; however, if 2 is substituted into the first inequality for y, the result is
. This cannot be true because the second inequality gives
.
\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+00:00","options":[{"label":"A","content_html":"