Browse Questions

Solve the inequality $6 \leq -3( 2x-4) < 12$

$\begin{array}{1 1}(A)\;(0,1]\\(B)\;[4,5]\\(C)\;[3,4]\\(D)\;[2,3]\end{array}$

Toolbox:
• Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
• Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
• If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $'>'$ sign changes to $'<'$ and $'<'$ changes $'>'$ .
The given inequality is $6 \leq -3(2x-4) < 12$
Dividing by a positive numbers 3, through out the inequality
=> $2 \leq -(2x-4) <4$
Dividing by a negative number -1 throughout inequality
=> $-2 \geq 2x-4 > -4$
Adding +4 to the inequality through out
$=> -2+ 4 \leq 2x-4+4 > -4+4$
$=> 2 \geq 2x > 0$
Dividing by 2 throughout $1 \geq x > 0$
$=> 1 \geq x >0$
Step 2:
All real number greater than or equal to 1 and less than 0 are solutions to the given inequality .
The solution set is $(0,1]$
Hence A is the correct answer.