inequality word problem

Question

The height in inches (h) of a tomatoe plant growing in a garden is given by the equation h=2x+3 where h represents time in days. When will the tomatoe plant be between 13 and 27 inches.

I can not figure it out.

 

a.  13 < +<27

b.  5<+<12

c.   6<+<12

 d.  +<12

Answer 1

Let's figure out when the tomato plant's height will be 13 inches. I think you meant to say x represents time in days. So, plug h = 13 into the equation and solve for x:

 

13 = 2x + 3

10 = 2x

5 = x

 

That means the tomato plant will reach 13 inches after x = 5 days. That number is our lower bound. Now, let's figure out when the height will be 27 inches. Plug h = 27 into the equation and solve for x:

 

27 = 2x + 3

24 = 2x

12 = x

 

That means the tomato plant will reach 27 inches after x = 12 days. That number is our upper bound. The tomato plant will be shorter than 13 inches before day 5 and taller than 27 inches after day 12, so it will be between 13 and 27 inches between day 5 and day 12.

 

You can write this as an inequality like so:

 

5 < x < 12

 

That inequality means that when x is between 5 and 12, the height will be between 13 and 27 inches.