Question

Penelope is playing a number game with her sister June. Penelope is thinking of a number and wants June to guess it. Five more than three times her number is between 5 and 38. Write a compound inequality that shows the range of numbers that Penelope might be thinking of.

Answer 1

Let her number be x

Five more than three times her number

First

times her number is

`3x`

Five more than three times her number is

`3x+5`

Her number is between 5 and 38

This implies

`5<3x+5<38`

Simplify the compound inequality

[tex]\begin{gathered} 5-5<3x<38-5 \\ \Rightarrow0<3x<33 \\ \Rightarrow0The inequality shows the range of numbers that Penelope might be thinking of.[tex]0