SOLUTION: Penelope is playing a number game with her sister June. Penelope is thinking of a number, x, and wants June to guess it. Five more than two times her number is between 3 and 17. Wr

Algebra ->  College  -> Linear Algebra -> SOLUTION: Penelope is playing a number game with her sister June. Penelope is thinking of a number, x, and wants June to guess it. Five more than two times her number is between 3 and 17. Wr      Log On


   

Question 1135617: Penelope is playing a number game with her sister June. Penelope is thinking of a number, x, and wants June to guess it. Five more than two times her number is between 3 and 17. Write a compound inequality that shows the range of numbers that Penelope might be thinking of.
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
The compound inequality you are asking for is


    3 <= 2x + 5 <= 17.


If you want to get its solution, then


a)  subtract 5 from all three components of the inequality


    3 - 5 <= 2x <= 17-5,   or

    -2    <= 2x <= 12


b)  divide by 2 all three components of the last inequality


     -1 <= x <= 6.


It is your ANSWER.  Penelope's number is between -1  and 6, inclusively.

Answered.

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On compound inequalities,  see the lesson
    - Solving compound inequalities
in this site.