Since two times a number decreased by four is between -14 and 32, we need to solve the following compound inequality:
[tex]-14<2x-4<32[/tex]In order to solve it, we can apply the same operations on all the parts of the inequality, until we isolate the variable x and find its value.
We obtain:
[tex]\begin{gathered} -14+4<2x-4+4<32+4 \\ \\ -10<2x<36 \\ \\ -\frac{10}{2}<\frac{2x}{2}<\frac{36}{2} \\ \\ -5Now, we need to write the answer using interval notation. Since x can't be -5 nor 18, only the values between them, the interval of valid values is:[tex](-5,18)[/tex]