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

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

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Updated on: 28 Sep 2018, 07:50
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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) $$-1 < g < 5$$

Originally posted by reynaldreni on 28 Sep 2018, 07:45.
Last edited by Bunuel on 28 Sep 2018, 07:50, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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28 Sep 2018, 08:10
2-g < 3
-g < 1
g > - 1

2-g > - 3
- g > - 5

g < 5

-1 < g < 5

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Posts: 52254
Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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28 Sep 2018, 08:21
reynaldreni wrote:
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) $$-1 < g < 5$$

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: $$5 > g > -1$$.

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 05:45
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

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 08:01
vipulshahi wrote:
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

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The above is correct.
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Posts: 2448
Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 14:55

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

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 14:58

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

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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16 Dec 2018, 04:22
Bunuel wrote:
reynaldreni wrote:
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) $$-1 < g < 5$$

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: $$5 > g > -1$$.

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
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Re: If (2-g)^2 < 9, which of the following expression of g is correct? &nbs [#permalink] 16 Dec 2018, 04:22
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