If |10y-4| 7 and y

Question

If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8 
B. -0.1 
C. 0.1 
D. 0 
E. 1

Bunuel · Accepted Answer

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following: |10y - 4| > 7 means that either 10y-4>7 (when y>\frac{4}{10} ) or -(10y-4)>7 (when y\leq{\frac{4}{10}} ). Solve both inequalities: 10y-4>7 --> y>1.1 . Since we are told that y<1 , then discard this solution. -(10y-4)>7 --> y<-0.3 . Only answer choice which is less than -0.3 is -0.8. Answer: A. Hope it's clear.

Narenn · Answer

In my opinion applying rules in modulus is much more easier than checking for multiple values. The rules are simple. 1) !x! < a -------> -a < x < a so if !x-a! < r then -r < x-a < r -------> a-r < x < a+r 2) !x! > a ------> either x > a or x < -a so if !X-a! > r then either x-a > r ------> x > a+r or x-a < -r -----> -x+a > r --------> x < a-r Regards, Abhijit

mehasingh · Answer

why cant we get an answer by simply substituting values in the equation |10y - 4| > 7

Bunuel · Answer

Actually we can, this would also be a correct approach.

rhallik · Answer

If I am not mistaken you have a typo in your explanation: 10y-4>7 shall be y>11/10 not y>4/10.

Bunuel · Answer

No typo there.

When  y>\frac{4}{10} , then we have  10y-4>7  -->  y>\frac{11}{10} .

When  y\leq{\frac{4}{10}} ), then we have  -(10y-4)>7  -->  y<-\frac{3}{10} .

Hope it's clear.

WholeLottaLove · Answer

If |10y - 4| > 7 and y < 1, which of the following could be y?

|10y - 4| > 7 
|10(-.8) - 4| > 7
|-8-4| > 7
|-12| > 7
|12| > 7
12 > 7

(A)

Nunuboy1994 · Answer

Bunuel  how are you getting the y > 4/10?

Bunuel · Answer

4/10 is a transition point for 10y-4 (transition point is a value of a variable for which expression in absolute value changes its sign).

When  y>\frac{4}{10} , then 10y - 4 > 0, so |10y - 4| = 10y - 4.

When  y\leq{\frac{4}{10}} , then 10y - 4 <= 0, so |10y - 4| = -(10y - 4).

shinrai15 · Answer

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following: |10y - 4| > 7 means that either 10y-4>7 (when y>\frac{4}{10} ) or -(10y-4)>7 (when y\leq{\frac{4}{10}} ). Solve both inequalities: 10y-4>7 --> y>1.1 . Since we are told that y<1 , then discard this solution. -(10y-4)>7 --> y<-0.3 . Only answer choice which is less than -0.3 is -0.8. Answer: A. Hope it's clear.[/quo How can u assume that the answer is -0.8 when get the solved answered as -0.3?? please explain @bunnel

Bunuel · Answer

We did not get that y = -0.3. We got that y < -0.3 (y is LESS than 0.3). -0.8 IS LESS than -0.3, so y could be -0.8

shinrai15 · Answer

Thank you @bunnel for clarifying..

Sumo23 · Answer

Solve the equation by taking out the modulus so we get 10y - 4 > 7 or 10y - 4 < -7.

On solving the equations as per the condition that y <0 we get that y < -3/10 I.e. y < -0.3; thus the only option that fits is -0.8, hence option A

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Mo2men · Answer

Plug-in answer choices into inequality

Let y = -0.8...........|10* -0.8 - 4| > 7.............|-12| > 7.......12 > 7

Answer: A

ishan261288 · Answer

If |10y - 4| > 7 and y < 1, which of the following could be y?
A little doubt here..

We can write this as

-7>(10y-4)>7

Add 4

-3> 10y>11

Divide by 10

-0.3>y>1.1

So y is between -0.3 to 1.1 and y is <1 as per question ------------> So why answer is A.

I am sure I am missing something but I don't know what..

Please explain Bunuel

RikitaDsouza · Answer

Posted from my mobile device

bumpbot · Answer

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If |10y-4| > 7 and y < 1, which of the following could be y?

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