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# Which of the following is equivalent to the pair of

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Manager
Joined: 02 Dec 2012
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Which of the following is equivalent to the pair of  [#permalink]

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13 Dec 2012, 09:47
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5% (low)

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97% (00:44) correct 3% (01:20) wrong based on 1956 sessions

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Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 < x < 16
(B) 2 <= x < 4
(C) 2 < x <= 8
(D) 4 < x <= 8
(E) 4 <= x <= 16
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Re: Which of the following is equivalent to the pair of  [#permalink]

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13 Dec 2012, 09:48
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Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 < x < 16
(B) 2 <= x < 4
(C) 2 < x <= 8
(D) 4 < x <= 8
(E) 4 <= x <= 16

x + 6 > 10 --> x > 4;
x - 3 <= 5 --> x<=8;

Therefore 4 < x <=8.

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Re: Which of the following is equivalent to the pair of  [#permalink]

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12 Sep 2014, 06:27
Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 < x < 16
(B) 2 <= x < 4
(C) 2 < x <= 8
(D) 4 < x <= 8
(E) 4 <= x <= 16

x + 6 > 10 and x - 3 <= 5

x>4 and x<=8 combining

4<x<=8
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Re: Which of the following is equivalent to the pair of  [#permalink]

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30 Sep 2014, 23:08
x > 4 & x< = 8

OR

4 < x & x < = 8

4 < x < = 8

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Re: Which of the following is equivalent to the pair of  [#permalink]

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25 May 2016, 21:54
2
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-25 at 9.43.26 PM.png [ 64.89 KiB | Viewed 20892 times ]

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Re: Which of the following is equivalent to the pair of  [#permalink]

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15 Jun 2016, 12:23
1
Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 < x < 16
(B) 2 <= x < 4
(C) 2 < x <= 8
(D) 4 < x <= 8
(E) 4 <= x <= 16

Solution:

Let’s isolate x in both inequalities, starting with x + 6 > 10.

x + 6 > 10

x > 4

Next we isolate x in the inequality x – 3  5.

x – 3 <= 5

x <= 8

Bringing these two inequalities together we know:

4 < x <= 8

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Re: Which of the following is equivalent to the pair of  [#permalink]

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02 Aug 2016, 07:05
2
Top Contributor
Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 < 5 ?

(A) 2 < x < 16
(B) 2 < x < 4
(C) 2 < x < 8
(D) 4 < x < 8
(E) 4 < x < 16

The above solutions are great. I just want to add one more tip.
When it comes to multiple inequalities, I find that it helps to rearrange them so that the inequality signs are all facing the same direction (I prefer arranging them so that the values are in ascending order from left to right)

So, x + 6 > 10 and x - 3 < 5 first become 10 < x + 6 and x - 3 < 5
For 10 < x + 6, we subtract 6 from both sides to get: 4 < x
For x - 3 < 5, we add 3 to both sides to get: x < 8
With the two inequality signs facing the same direction, it's easy to combine them to get 4 < x < 8

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Re: Which of the following is equivalent to the pair of  [#permalink]

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25 Mar 2017, 12:21
x>4
x<=8
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Joined: 12 Sep 2015
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Which of the following is equivalent to the pair of  [#permalink]

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28 Aug 2017, 13:33
Top Contributor
Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 ≤ 5 ?

(A) 2 < x < 16
(B) 2 ≤ x < 4
(C) 2 < x ≤ 8
(D) 4 < x ≤ 8
(E) 4 ≤ x ≤ 16

Another approach is to eliminate 4 of the answer choices

First, x + 6 > 10 can be rewritten as x > 4
This means that x CANNOT equal 3
When we check the answer choices, we see that A, B and C all say that x COULD equal 3
So, eliminate A, B and C

Second, x - 3 ≤ 5 can be rewritten as x ≤ 8
This means that x CANNOT equal 9
When we check the remaining answer choices, we see that E says that x COULD equal 9
So, eliminate E

We're left with answer choice D

Cheers,
Brent
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Re: Which of the following is equivalent to the pair of  [#permalink]

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10 Mar 2019, 15:17
[1] Simplify

$$x + 6 > 10$$

$$\Rightarrow x > 4$$

$$x - 3 \le 5$$

$$\Rightarrow x \le 8$$

[2] Combine

$$4< x \le8$$

Re: Which of the following is equivalent to the pair of   [#permalink] 10 Mar 2019, 15:17
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