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

Question

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

anonymous · Answer

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.

anonymous · Answer

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.

anonymous · Answer

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).

anonymous · Answer

Choose x=0.  Then$$27-6(0-10)>^?-3(0)+26 \rightarrow 87>^?26$$ True. So x<61/3 is one region.

anonymous · Answer

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.

anonymous · Answer

Your solution is all x less than 61/3.