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Solve the "or" compound inequality 5-x>=7 or 8x-3> 29

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awlgeelady | Student, Undergraduate | Honors

Posted February 5, 2013 at 2:00 PM via web

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Solve the "or" compound inequality

5-x>=7 or 8x-3> 29

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 5, 2013 at 2:13 PM (Answer #1)

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Since the information provided by the problem is incomplete because the inequality 8x - 3> does not specify what is to the right side.

Considering as a second inequality `8x - 3 > 5` yields:

`5 - x >= 7 or 8x - 3 > 5`

You need to solve each inequality separately, such that:

`5 - x >= 7 => -x >= 7 - 5 => -x >= 2`

You need to multiply by `-1` switching the direction of inequality, such that:

`x <= -2 => x in (-oo,-2]`

Solving the second inequality yields:

`8x - 3 > 5 => 8x > 3 + 5 => 8x > 8 => x > 1`

`x in (1,oo)`

You should remember that the solution to the "or" compounded inequality is the reunion of intervals `x in (-oo,-2] U (1,oo).`

Hence, evaluating the interval solution to the given compounded inequality yields `x in (-oo,-2] U (1,oo).`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 5, 2013 at 6:16 PM (Answer #2)

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It is given that `5-x>=7` or `8x-3> 29`

`5-x>=7` or `8x-3> 29`

=> `5 - 7 >= x` or `8x > 32`

=> `-2 >= x` or `x > 4`

The set that satisfies these inequalities is `(4, oo)U[-2, -oo)`

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awlgeelady | Student, Undergraduate | Honors

Posted February 5, 2013 at 2:22 PM (Answer #3)

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29 is the number that came after the 3

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