If (2-g)^2

Question

If  (2-g)^2 < 9 , which of the following expression of  g  is correct?

A)  g < -1

B)  -3/\sqrt{2}< g <3/\sqrt{2}

C)  -9/2 < g < 9/2

D)  g > 5

E)  -1 < g < 5

Salsanousi · Answer

2-g < 3 -g < 1 g > - 1 2-g > - 3 - g > - 5 g < 5 -1 < g < 5 Answer choice E Posted from my mobile device

Bunuel · Answer

Take the square root from both ides of (2-g)^2 < 9 (note that we can safely do that sine both sides are non-negative): |2 - g| < 3 ; Get rid of the modulus: -3 < 2 - g < 3 ; Subtract 2: -5 < -g < 1 ; Multiply by -1 and flip the signs: 5 > g > -1 . Answer: E.

vipulshahi · Answer

Dear  Bunuel ,

Please review my approach is it okay ?

(2-g)^2 < 9
(g-2)^2 < 9
(g-2)^2 -9 <0
(g-2)^2 - 3^2 < 0
Now applying (a^2 - b^2) = (a+b)(a-b)

(g-2+3)(g-2-3)<0
(g+1)(g-5)<0

Now putting on number line , we will get 
-1<g<5

Posted from my mobile device

Bunuel · Answer

____________________________
The above is correct.

EgmatQuantExpert · Answer

Answer: B

Solution

Given:

•  (2−g)^2<9

To find:  
• The correct expression of g

Approach and Working out:

Method-1)

•  (2−g)^2-9 <0 
•  (2-g)^2 – 3^2 <0 
• (2-g-3) (2-g+3)<0
• (-1-g)(5-g) <0
• (g+1)(g-5)<0
• -1 < g < 5

Answer: E

EgmatQuantExpert · Answer

Solution Given: • (2−g)^2<9 To find: • The correct expression of g Approach and Working out: Method-2) • |(2−g)|< 3 • -3 < (2-g) < 3 • -5 < -g < 1 • 5> g > -1 Answer: E

gota900 · Answer

Dear  Bunuel ,

I have issues with this "since both sides are non-negative". I came across this assumption for several times now. Most often in the module regarding absolute values. However, I already didn't get to the real bottom of the issue. May you elaborate your thought behind "since both sides are non-negative"?

I would like to add the following: I understand that distances in general can't be negative and that absolute values can be interpreted as distances! However, even after understanding that fact, I still don't understand, situations like the following:

|x-y|

In my understanding, this would simply be some distance from point x to y on a number line. But we can't say foe sure that this is expression will yield some positive value, because we don't know either value of x or y. Why is that?

Best, gota900

bumpbot · Answer

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If (2-g)^2 < 9, which of the following expression of g is correct?

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