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BrushMyQuant
Given that \(6 < 2x – 4 < 12\) and we need to find a possible value of x out of the answer choices

\(6 < 2x – 4 < 12\)
Adding 4 on all the sides we get

6 + 4 < 2x - 4 + 4 < 12 + 4
=> 10 < 2x < 16
Dividing by 2 on all the sides we get
=> 5 < x < 8
=> 7 is a possible value of x

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Inequalities

BrushMyQuant

Thank you for this helpful response.

To clarify, because we first add 4 to both sides before dividing by 2, do the rules of PEMDAs (order of operations) apply only to linear equations and NOT to inequalities?
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woohoo921 : We added 4 to both the sides before dividing by 2 to make sure that the middle part of the inequality is a term only in x. This does not violate the rule of PEMDAS as division was not there to start with. We added a number(4) first. Finished addition (division is not there in the frame till now) and then divided a number (2). So, this still follows rule of PEMDAS.

Rules of PEMDAS will apply to inequality also. We will apply those rules on both sides of the inequality separately. (like we do for equalities)

- We can add, subtract, multiply and divide (by positive number) both the sides of the inequality without changing the sign of the inequality
- When we multiple a negative number on both sides of the inequality then the sign reverses. (ex. if sign was > then it becomes < and vice versa)


Hope it helps!
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