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anonymous

  • 5 years ago

How do we do this Solve 27-6(x-10)>-3x+26

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  1. anonymous
    • 5 years ago
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    Set the inequality to an equality and solve for x. This will determine the boundary of your intervals. You then take a test point from each interval to see if the inequality is satisfied in that region. If the test point works, all x-values in that region form part of your solution. If the test point doesn't work, the region isn't included.

  2. anonymous
    • 5 years ago
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    So\[27-6x+60=-3x+26\]yields\[27-26+60=-3x+6x \rightarrow 61=3x\]that is,\[x=\frac{61}{3}\]is the boundary point.

  3. anonymous
    • 5 years ago
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    You only have one point, so the number line will be broken into two regions: all those x such that x<61/3 and all those x such that x>61/3 (note 61/3 is not included since you have a strict inequality).

  4. anonymous
    • 5 years ago
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    Choose x=0. Then\[27-6(0-10)>^?-3(0)+26 \rightarrow 87>^?26\] True. So x<61/3 is one region.

  5. anonymous
    • 5 years ago
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    For completeness check the other: x>61/3. Choose 100. Then\[27-6(100-10)>^?-3(100)+26 \rightarrow -513>^?-274\]False. So x>61/3 is not a solution.

  6. anonymous
    • 5 years ago
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    Your solution is all x less than 61/3.

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