anonymous 5 years ago How do we do this Solve 27-6(x-10)>-3x+26

1. anonymous

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

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

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

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

5. anonymous

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

Your solution is all x less than 61/3.