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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 7x > 4 + 5x
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16 Feb 2022, 07:00
16 Feb 2022, 07:00
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Question Stats:
77% (01:40) correct
22% (01:57) wrong based on 18 sessions
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If \(7x > 4 + 5x\), and \(3 – 2x < -x + 4 < 7.8 – 2x\), what is the value of the integer \(x\)?
Show: ::
Answer: 3
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 7x > 4 + 5x
[#permalink]
16 Feb 2022, 07:41
16 Feb 2022, 07:41
1
Carcass wrote:
If \(7x > 4 + 5x\), and \(3 – 2x < -x + 4 < 7.8 – 2x\), what is the value of the integer \(x\)?
Show: ::
Answer: 3
Take: 7x > 4 + 5x
Subtract 5x from both sides: \(2x > 4\)
Divide both sides by 2 to get: \(x > 2\)
Since we are told x is an integer, the possible values of x are: 3, 4, 5, 6, 7,...
Now take: 3 – 2x < -x + 4 < 7.8 – 2x
Add 2x to all three parts: 3 < x + 4 < 7.8
Subtract 4 from all three parts: -1 < x < 3.8
So, the possible values of integer x are: 0, 1, 2 and 3
Since the x-value must satisfy both inequalities, the correct answer must be x = 3
Answer: 3
