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If (7 - 2y)/3 < -5 then

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If (7 - 2y)/3 < -5 then  [#permalink]

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New post 12 Aug 2018, 08:49
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (00:20) correct 23% (00:42) wrong based on 40 sessions

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If \(\frac{7 - 2y}{3} < -5\) then

1. y < -4

2. y < 11

3. y > -4

4. y > 4

5. y > 11

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Re: If (7 - 2y)/3 < -5 then  [#permalink]

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New post 12 Aug 2018, 09:54
AkshdeepS wrote:
If \(\frac{7 - 2y}{3}\) \(< -5\) then

1. y < -4

2. y < 11

3. y > -4

4. y > 4

5. y > 11


Given, \(\frac{7 - 2y}{3}\) \(< -5\)
Or, 7-2y<-15
Or, -(2y-7)<-15
Or, 2y-7>15
Or, 2y>22
Or, y>11

Ans. (E)
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If (7 - 2y)/3 < -5 then  [#permalink]

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New post 13 Aug 2018, 07:46
AkshdeepS wrote:
If \(\frac{7 - 2y}{3} < -5\) then

1. y < -4

2. y < 11

3. y > -4

4. y > 4

5. y > 11

The trap answer is B.

Rule: If we divide an inequality by a negative number, we must flip the inequality sign.

\(\frac{7 - 2y}{3} < -5\)

\(7 - 2y < -15\)

\(- 2y < -22\)

Divide both sides by \(-2\). Flip the sign.

\(\frac{- 2y}{-2} <\frac{-22}{-2}\)

\(y > 11\)

Answer E

Corollary: Never divide an inequality by a variable unless that variable must be positive, such as \(x^2\).

Here is a good explanation for "why flip the sign" that uses the properties of the number line and is followed by an easy algebraic proof.
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Re: If (7 - 2y)/3 < -5 then  [#permalink]

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New post 13 Aug 2018, 08:51
AkshdeepS wrote:
If \(\frac{7 - 2y}{3} < -5\) then

1. y < -4

2. y < 11

3. y > -4

4. y > 4

5. y > 11


\(\frac{7 - 2y}{3} < -5\)

Or, \(7 - 2y < -15\)

Or, \(7 + 15 < 2y\)

Or, 1\(1 < y\), Thus Answer must be (E)
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Re: If (7 - 2y)/3 < -5 then  [#permalink]

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New post 18 Aug 2018, 18:27
AkshdeepS wrote:
If \(\frac{7 - 2y}{3} < -5\) then

1. y < -4

2. y < 11

3. y > -4

4. y > 4

5. y > 11


Simplifying, we have:

7 - 2y < -15

-2y < -22

y > 11

Answer: 5/E
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Re: If (7 - 2y)/3 < -5 then &nbs [#permalink] 18 Aug 2018, 18:27
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