Question

$6x-9y>12$
Which of the following inequalities is equivalent to the inequality above?

• A. $x-y>2$
• B. $2x-3y>4$
• C. $3x-2y>4$
• D. $3y-2x>2$

Answer 1

The correct option is B $2x-3y>4$

We know that an inequality remains unchanged if the entire inequality is multiplied by a positive constant. If an inequality is multiplied by a positive constant, the ratios of the coefficients of x, coefficients of y and the constant terms will be equal.
It can be observed that in option B,
Ratio of coefficients of $x=\frac{6}{2}=3$
Ratio of coefficients of $y=\frac{-9}{-3}=3$
Ratio of constant terms =$\frac{12}{4}=3$
Hence, B is the correct choice.