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If x>5 and (4x+y)=8, which of the following must be true?
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12 Sep 2022, 20:05
12 Sep 2022, 20:05
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If x>5 and (4x+y)=8, which of the following must be true?
[A] y<-10
[B] y=-12
[C] y>10
[D] y>-12
[E] y<-14
I get to y<-12, so I guessed that since y<-12<-10 then y<-10 must be true. But other classmates say y<-14 is the correct answer because of the domain of the inequality. What do you think is the correct answer?
[A] y<-10
[B] y=-12
[C] y>10
[D] y>-12
[E] y<-14
I get to y<-12, so I guessed that since y<-12<-10 then y<-10 must be true. But other classmates say y<-14 is the correct answer because of the domain of the inequality. What do you think is the correct answer?
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If x>5 and (4x+y)=8, which of the following must be true?
[#permalink]
14 Sep 2022, 06:36
14 Sep 2022, 06:36
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1
Given that x>5 and (4x+y)=8 and we need to find which of the following is correct
4x + y = 8
=> 4x = 8 - y
=> x = \(\frac{8}{4}\) - \(\frac{y}{4}\) = 2 - \(\frac{y}{4}\)
Now, x > 5
=> 2 - \(\frac{y}{4}\) > 5
=> \(\frac{y}{4}\) < 2 - 5
=> y < -3*4
=> y < -12
Now, if we look at the answer choices then only two answer choices stand out
y < -10 and y < -14
y < -14 is incorrect because it DOES NOT CONTAIN all the values which are in the range of y < -12
Ex.: y = -13 which is in the range of y < -12 but not in y < -14
y < -10 on the other hand CONTAINS all the solutions in the range of y < -12
See below image to visualize why y < -10 is correct as
-10 to -14.png [ 4.67 KiB | Viewed 1037 times ]
-> Given that y < -12 then it is implied that y < -10 also, as y < -10 contains y < -12
-> Given that y < -12 then it is NOT necessary that y < -14 as y can very well be -13
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Inequalities
4x + y = 8
=> 4x = 8 - y
=> x = \(\frac{8}{4}\) - \(\frac{y}{4}\) = 2 - \(\frac{y}{4}\)
Now, x > 5
=> 2 - \(\frac{y}{4}\) > 5
=> \(\frac{y}{4}\) < 2 - 5
=> y < -3*4
=> y < -12
Now, if we look at the answer choices then only two answer choices stand out
y < -10 and y < -14
y < -14 is incorrect because it DOES NOT CONTAIN all the values which are in the range of y < -12
Ex.: y = -13 which is in the range of y < -12 but not in y < -14
y < -10 on the other hand CONTAINS all the solutions in the range of y < -12
See below image to visualize why y < -10 is correct as
Attachment:
-10 to -14.png [ 4.67 KiB | Viewed 1037 times ]
-> Given that y < -12 then it is implied that y < -10 also, as y < -10 contains y < -12
-> Given that y < -12 then it is NOT necessary that y < -14 as y can very well be -13
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Inequalities
If x>5 and (4x+y)=8, which of the following must be true?
[#permalink]
14 Sep 2022, 07:52
14 Sep 2022, 07:52
2
BrushMyQuant
But y<-10 does contain all numbers in y<-12. y=-11<-10.
In contrast, y<-14 does not include all numbers in y<-12 (the inverse is true though). Y could be -13 for example.
I'm not sure whether the question is asking for a subset of y<-12 or if we need to find a set that includes y<-12
But y<-10 does contain all numbers in y<-12. y=-11<-10.
In contrast, y<-14 does not include all numbers in y<-12 (the inverse is true though). Y could be -13 for example.
I'm not sure whether the question is asking for a subset of y<-12 or if we need to find a set that includes y<-12
