SOLUTION: Solve. 9/10(3+2x) +2>_ 23 The solution is {xlx ? ?} (of course _ is supposed to be under >) Will someone please help me with this one?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve. 9/10(3+2x) +2>_ 23 The solution is {xlx ? ?} (of course _ is supposed to be under >) Will someone please help me with this one?      Log On


   

Question 143890: Solve.
9/10(3+2x) +2>_ 23
The solution is {xlx ? ?} (of course _ is supposed to be under >)
Will someone please help me with this one?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%289%2F10%29%283%2B2x%29%2B2%3E=23

Solve this just the same way you would solve it if it were an equation instead of an inequality, except that if you have to multiply or divide by a negative number, you must reverse the sense of the inequality.

%289%2F10%29%283%2B2x%29%3E=21
9%283%2B2x%29%3E=210
27%2B18x%3E=210
18x%3E=183
x%3E=61%2F6

Check:
%289%2F10%29%283%2B2%2861%2F6%29%29%2B2%3E=23
%289%2F10%29%2818%2F6%2B122%2F6%29%2B2%3E=23
%289%2F10%29%28140%2F6%29%2B2%3E=23
%281260%2F60%29%2B2%3E=23
%281380%2F60%29=23, so the equals part is ok.

Since 61%2F6 is a little bigger than 10, pick a larger number, say 27%2F2.
%289%2F10%29%283%2B2%2827%2F2%29%29%29%2B2%3E=23
%289%2F10%29%2830%29%2B2%3E=23
27%2B2=29%3E23, so the greater than part works.

Now pick a smaller number, say 17%2F2
%289%2F10%29%283%2B2%2817%2F2%29%29%29%2B2%3E=23
%289%2F10%29%2820%29%2B2%3E=23
18%2B2=20%3C23, so a smaller number makes the relationship fail. Answer checks.