3<8+5/6x<18

Question

Solve the inequality then write the answer in set notation.

Answer 1

There are several ways that I could interpret the problem that you wrote.  I have interpreted it as below.  Please let me know if I should understand it differently.

3 < 8 + (5/6)x < 18                     Given equation

3 - 8 < 8 + (5/6)x - 8 < 18 - 8      Subtract 8 from all 3 parts

-5 < (5/6)x < 10                          Simplify

-5(6/5) < (5/6)x(6/5) < 10(6/5)    Multiply by 6/5

-6 < x < 12                                 Simplify

{x ι -6 < x < 12}