Question

19. Write an inequality to represent the relationship described and solve.Three-fourths of a number plus five is less than one-half of that number.

Answer 1

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:

`(3)/(4)x+5<(1)/(2)x`

We can solve it as:

`\begin{gathered} (3)/(4)x+5<(1)/(2)x \\ (3)/(4)x-(1)/(2)x+5<0 \\ ((3)/(4)-(1)/(2))x<-5 \\ ((3)/(4)-(2)/(4))x<-5 \\ (1)/(4)x<-5 \\ x<-5\cdot4 \\ x<-20 \end{gathered}`

Answer: the number is less than -20.