Identify the steps needed to change the first inequality into the second. $3 x - 4 y 12$ to $y

Question

Identify the steps needed to change the first inequality into the second. $3 x - 4 y > 12$ to $y < \frac { 3 x } { 4 } - 3$
A) Subtract 3x from both sides.
Divide both sides by -4 and reverse inequality sign.
B) Subtract 3x from both sides.
Divide both sides by 4 and reverse inequality sign.
C) Add 4y to both sides.
Divide both sides by -3 and reverse inequality sign.
D) Add 4y to both sides.
Divide both sides by 3 and reverse inequality sign.
E) Add 4y to both sides.
Divide both sides by 3.

Quizplus · Accepted Answer

To change $3x - 4y > 12$ into $y < \frac{3x}{4} - 3$, you first add 4y to both sides to isolate y terms on one side, resulting in $3x > 4y + 12$. Then, you divide everything by 4 (not -4, because we're not dividing by -y), and to keep the inequality direction correct, no need to reverse the sign since we're not multiplying or dividing by a negative number. This results in $y < \frac{3x}{4} - 3$, which matches none of the provided steps exactly, indicating a mistake in the selection process. The correct process aligns most closely with option E, but due to a misunderstanding in explaining the correct answer, the initial selection was incorrect. The correct steps are indeed to add 4y to both sides and then divide by 4, but there was confusion in the explanation regarding the reversal of the inequality sign, which is not necessary in this case because we are not dividing by a negative number.

Identify the Steps Needed to Change the First Inequality into the Second