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If x + 5 > 2 and x - 3 < 7, the value of x must be between

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Walkabout
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If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   03 Dec 2012, 04:11
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If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10
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Bunuel
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   03 Dec 2012, 04:12
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If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10

x + 5 > 2 --> x>-3;
x - 3 < 7 --> x<10.

Therefore, the value of x must be between -3 and 10 (-3<x<10).

Answer: A.
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   27 May 2016, 05:40
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Walkabout wrote:
If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10


Let’s isolate x in each inequality.

x + 5 > 2

x > -3

Next we simplify x – 3 < 7.

x – 3 < 7

x < 10

We know that x is greater than -3 and less than 10.

The answer is A.
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   27 May 2016, 05:57
Walkabout wrote:
If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10


x+5 > 2
taking 5 on other side, we get: x > 2-5; x > -3

x - 3 < 7

taking -3 on other side, we get: x > 3+7; x > 10

x lies between -3 and 10

Option A is correct answer.
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   05 Jul 2016, 06:24
Walkabout wrote:
If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10




x+5>2 ==>x>-3
x-3<7 ==> x<10
-3<x<10
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   19 Jul 2020, 13:49
there's something I still dont get, how is possible for X to be -3.

If you replace: X+5>2 ==> -3+5>2 ==> 2>2 ¿2 is not higher than 2? the right answer should be "=" not ">" the same for the another.
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   10 Jun 2021, 23:26
the two inequalities clearly suggests that x>-3 and x<10
therefore the valuve of x will be between -3 and 10 (A)
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   11 Jun 2021, 01:21
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When the word ‘And’ used in conjunction with two inequalities, we need to find a range that satisfies both inequalities – in short, we have to find a common range.

x + 5 > 2. Subtracting 5 from both sides, the inequality can be rewritten as x > -3.
x – 3 < 7. Adding 7 to both sides, the inequality can be rewritten as x < 10.

Note that adding / subtracting the same number to / from both sides of an inequality does not change the inequality sign.

Since we are looking for a range that will satisfy both, we can say that -3<x<10. Therefore, x has to be between -3 and 10.

The correct answer option is A.

Hope that helps!
Aravind B T
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   11 Jun 2021, 01:28
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Alvarito wrote:
there's something I still dont get, how is possible for X to be -3.

If you replace: X+5>2 ==> -3+5>2 ==> 2>2 ¿2 is not higher than 2? the right answer should be "=" not ">" the same for the another.



Hello Alvarito,

As you have observed, the range of x that satisfies both the inequalities is -3<x<10.

-3<x means the number -3 is lesser than x; in other words, x is more than -3. You cannot take x = -3.

Additionally, the question is very clear in what it asks: the value of x is between which pairs of numbers. When you use the word ‘between’ you do not consider the extremities.

Try to work on leveraging language clues.

Hope that helps!
Aravind B T
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink] New post   20 Aug 2023, 00:45
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Re: If x + 5 > 2 and x - 3 < 7, the value of x must be between [#permalink]
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