Browse Questions

# Solve the inequality : $2 \leq 3x-4 \leq 5$

$\begin{array}{1 1}(A)\;[2,8]\\(B)\;[4,5]\\(C)\;[3,4]\\(D)\;[2,3]\end{array}$

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 $'>'$ .
Step 1:
The given inequality is $2 \leq 3x-4 \leq 5$
Adding $+4$ throughout the inequality $2+4 \leq 3x -4 +4 \leq 5+4$
=> $6 \leq 3x \leq 9$
Dividing by positive number 3 through out the inequality $=> 2 \leq x \leq 3$
$=> 2 \leq x \leq 3$
Step 2:
Thus all real number , which are greater than or equal to 2, and less than or equal to 3, are solutions to the given inequality .
The solution set is $[2,3]$
Hence D is the correct answer.
edited Aug 1, 2014 by meena.p