If 2x

Question

If 2x < p – 10 and |p| < 6, which of the following cannot be a value of x ?

A. -9
B. -7
C. -5
D. -3
E. -2

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ankushsambare · Answer

Given:
2x < p − 10
and |p| < 6 → so −6 < p < 6
so p − 10 ranges between:
−6 − 10 = −16
6 − 10 = −4
so:
 −16 < p − 10 < −4

We need 2x < p − 10, 
so 2x must be less than some number between −16 and −4
this is possible as long as 2x < −4 (because the largest p − 10 can be is just below −4)
so:
2x < −4
 x < −2
so x must be strictly less than −2
 
check options:
−9 < −2 → possible
−7 < −2 → possible
−5 < −2 → possible
−3 < −2 → possible
−2 is not less than −2 → not possible

Final answer: E

Adit_ · Answer

Option E  correctly demonstrates the inequalities represented in the stem.

dp1234 · Answer

|p|<6
-6<p<6 , Sub -10 from all
-16 < p-10 < -4

Now 2x<p-10. Thus 2x<-4 will give all values of x. 
x <-2 is solution. 
Clearly x=-2 isn't a solution.

Soln. E

ExpertsGlobal5 · Answer

E is the correct answer choice.

Video explanation:

https://www.youtube.com/watch?v=Fbto1VI46As

If 2x < p 10 and |p| < 6, which of the following cannot be a value

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