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 Post subject: what values of x that satisfy I5-2xI<=(less than equal to) 7Posted: Thu, 15 Sep 2011 00:12:42 UTC
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Joined: Wed, 17 Aug 2011 23:43:31 UTC
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How do we solve inequalities such as the one mentioned above where there is absolute value?

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 Post subject: Re: what values of x that satisfy I5-2xI<=(less than equal tPosted: Thu, 15 Sep 2011 00:25:01 UTC
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Joined: Fri, 1 Jul 2011 01:17:26 UTC
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You can rewrite it as -7 ≤ 5 - 2x ≤ 7.
-12 ≤ -2x ≤ 2, 12 ≥ 2x ≥ -2, 6 ≥ x ≥ -1.

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 Post subject: Re: what values of x that satisfy I5-2xI<=(less than equal tPosted: Thu, 15 Sep 2011 05:38:41 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
mathematic wrote:
You can rewrite it as -7 ≤ 5 - 2x ≤ 7.
-12 ≤ -2x ≤ 2, 12 ≥ 2x ≥ -2, 6 ≥ x ≥ -1.

Square both sides.

, divide that annoying 4 out:

factor:

From here it's easy.

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 Post subject: Re: what values of x that satisfy I5-2xI<=(less than equal tPosted: Thu, 15 Sep 2011 22:57:19 UTC
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mathematic wrote:
You can rewrite it as -7 ≤ 5 - 2x ≤ 7.
-12 ≤ -2x ≤ 2, 12 ≥ 2x ≥ -2, 6 ≥ x ≥ -1.

Square both sides.

, divide that annoying 4 out:

factor:

From here it's easy.

It's a matter of opinion, but I think my way is easier.

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 Post subject: Re: what values of x that satisfy I5-2xI<=(less than equal tPosted: Thu, 15 Sep 2011 23:57:36 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
mathematic wrote:
mathematic wrote:
You can rewrite it as -7 ≤ 5 - 2x ≤ 7.
-12 ≤ -2x ≤ 2, 12 ≥ 2x ≥ -2, 6 ≥ x ≥ -1.

Square both sides.

, divide that annoying 4 out:

factor:

From here it's easy.

It's a matter of opinion, but I think my way is easier.

Cases are almost never easier, this way it is absolutely immediately clear what the intervals are. And in any case it's senseless to talk about it, both are available to the op to choose as he likes, this isn't a popularity of solutions contest.

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