logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities
0 votes

Solve the inequality $-3 \leq 4 - \large\frac{7x}{2} $$ \leq 18$

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

Can you answer this question?
 
 

1 Answer

0 votes
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 $-3 \leq 4 - \large\frac{7x}{2} $$ \leq 18$
Adding -4 through out the inequality $=> -3-4 \leq 4 - \large\frac{7x}{2} $$-4 \leq 18-4$
=> $ -7 \leq \large\frac{-7x}{2} $$ \leq 14$
Multiplying by a negative number -2 through out
$=> 14 \geq 7x \geq -28$
Dividing by 7 through out the inequality => $ 2 \geq x \geq -4$
Step 2:
All numbers less than or equal to 2 and greater than or equal to -4 are solutions to given inequality .
The solution set is $[-4,2]$
Hence B is the correct answer.
answered Aug 1, 2014 by meena.p
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...