Question

When we multiply 2$\le x<4$ by $-4$; inequation becomes ___.

• A. -8$\le -4x<16$
• B. -8 $<-4x\le 16$
• C. $-16\le -4x<-8$
• D. -8 $>-4x\ge 16$

Answer 1

The correct option is C $-16\le -4x<-8$

Given: $2\le x<4$

Rule: If both the sides of an inequation are multiplied or divided by the same negative number, then the sign of the inequality will get reversed.
On multiplying the above inequation by $-4$, we get

$\Rightarrow (2\le x<4)\times (-4)$

$\Rightarrow -16\le -4x<-8$

Hence, correct option is D. $-16\le -4x<-8$.