We call the number x.
We know that three fourths of x plus 5 is less than one half of x.
This is a inequality that can be written as:
[tex]\frac{3}{4}x+5<\frac{1}{2}x[/tex]We can solve it as:
[tex]\begin{gathered} \frac{3}{4}x+5<\frac{1}{2}x \\ \frac{3}{4}x-\frac{1}{2}x+5<0 \\ (\frac{3}{4}-\frac{1}{2})x<-5 \\ (\frac{3}{4}-\frac{2}{4})x<-5 \\ \frac{1}{4}x<-5 \\ x<-5\cdot4 \\ x<-20 \end{gathered}[/tex]Answer: the number is less than -20.
