The multiplicative inverse of a number x is a number y such that their product xy is 1.
So, we want a number such that
[tex]-\dfrac{3}{8}\cdot x = 1[/tex]
Multply both sides by 8:
[tex]-3x=8[/tex]
Divide both sides by 3:
[tex]-x=\dfrac{8}{3}[/tex]
Change sign to both sides:
[tex]x=-\dfrac{8}{3}[/tex]
