Question

Compare the quantities in Column A and Column B Column A Column B The solutions of 4x - 30 2-3x + 12 The solutions (A) The quantity in Column A is greater. (B) The quantity is Column B is greater. (C) The quantities are equal. (D) The relationship cannot be determined from the inform

Answer 1

Column A:

$4x-30\ge-3x+12$

The solution will be as following :

$\begin{gathered} 4x+3x\ge12+30 \\ 7x\ge42 \\ \frac{7x}{7}\ge\frac{42}{7} \\ \\ x\ge6 \end{gathered}$

Column B:

$\frac{1}{2}x+3<-2x-6$

The solution will be as following :

$\begin{gathered} \frac{1}{2}x+2x<-6-3 \\ 2\frac{1}{2}x<-9 \\ \frac{5}{2}x<-9 \\ \\ x<-9\cdot\frac{2}{5} \\ \\ x<-3.6 \end{gathered}$

Compare the quantities in Column A and Column B

so,

$x\ge6\text{ and x < -3.6}$

So, the answer is option A) The quantity in Column A is greater.