Question

Hello could anyone help me out? thank you! The room temperature is 50 *F. The temperature will decrease by 4*F each hour. Let "h" be the number of hours. When will the temperature be below 32*F?

Write an inequality for this problem.

Answer 1

After 1 hour 46

After 2 hour 42

After 3 hour38

After 4 hour 34

After 4 (1/2) hour 32

Answer 2

We start off with 50 as our room temperature.

Then we subtract off 4h to indicate the temperature drops 4 degrees per hour

You can think of it like this

1 hour = drop by 4 degrees

h hours = drop by 4h degrees (multiply both sides by h)

So the expression 50-4h represents the temperature after h hours. We want this to be below 32, so 50-4h < 32 is the inequality we're after

Solving for h leads to

50-4h < 32

-4h < 32-50 ... subtract 50 from both sides

-4h < -18

h > -18/(-4) ... divide both sides by -4; note the inequality sign flips

h > 4.5

If you go beyond 4.5 hours, then the temperature will be below 32 degrees

notes:

• 4.5 hours = 4 hours, 30 minutes = 270 minutes
• the inequality sign flips whenever you divide both sides by a negative number