Algebra - Word Problem

Question

When a student subtracts 7 from a number, the result is greater than 5/3 of that number. Let x be the number. Represent this expression as an inequality that would answer the next question: What are the possible values of x? Be sure to simplify!

Answer 1

Alright, April, I like your name. Let's see if we can figure this out.

x = the number.  Then x - 7 > (5/3)x  ----> whenever you see the word "of" it means to multiply.

 

Let's get rid of the fraction and multiply everything by the denominator.

 

3x - 21 > 5x

 

      -2x > 21

 

Now, when we divide by a negative number, -2 in this case, we switch the sign!

 

         x < -21/2 (or -10 1/2 or -10.5)

 

Let's check. Let's pick a number less than -10 1/2, like -12.  

 

-12 - 7 > (5/3)(-12)

      -19 > -60/3

      - 19 > -20

 

Check!

 

So, the second part of our answer is x can be any number less than -10 1/2.

 

Hope this helps!