Question

Write a compound inequality for each situation 15. the scores on the last test range from 25% to 98%14. children and senior citizens receive a discount on tickets at the movie theater to receive a discount a person must be under 8 years old, or 70 years or older.

Answer 1

(15) The compound inequality shall involve one variable but with more than one constant. If the scores from the last test ranges from 25 to 98, that means if the score was x, then all the values of x is either equal to or greater than 25. At the same time, all the values of x are less than or equal to 98. So no one scored less than 25, but some scored 25. Then no one scored above 98, but the highest score was 98. Therefore;

`\begin{gathered} 25\subseteq x\subseteq98 \\ \text{That is, 25 is less than or equal to x, and x is less than or equal to 98} \end{gathered}`

(14) To receive a discount, a person must be under 8 years old, OR 70 years or older. In this instance a person must be under 8 years old simply means 8-year olds are NOT INCLUDED. The other condition is you must be 70 years or older, which means, the person is either 70 years or any age above 70 years (that is 70 IS INCLUDED). Hence you have;

`\begin{gathered} 8\supset x\supseteq70 \\ \text{That is 8 is greater than x and x is greater than or equal to 70} \\ \text{Please note that x}\subset8\text{ is also written in reverse form as 8}\supset x \end{gathered}`