THE AVERAGE WIND SPEED INCREASED 19 MILES/H FROM 8 AM TO 12 NOON. THE AVERAGE WIND SPEED DECREASED 5 MI MI/H FROM 12 NOON TO 4 PM. AT 4 PM, THE AVERAGE WIND SPEED WAS AT LEAST 32 MI/H. WHAT IS THE MINIMUM VALUE OF THE AVERAGE WIND SPEED AT 8 AM? NEED TO SOLVE AN INEQUALITY THAT MODELS SITUATION. THANKS

First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.

X + 19 - 5 ≤ 32

32 -19 + 5 ≥ x

Well, well, looks like we have a wind speed puzzle. Hold on to your hat, because here I go!

Let's call the average wind speed at 8 am "x" (in miles per hour).

From 8 am to 12 noon, the speed increased by 19 miles per hour, so at 12 noon, it would be x + 19 mph. Are you still with me?

Then, from 12 noon to 4 pm, the speed decreased by 5 miles per hour. So at 4 pm, it would be (x + 19) - 5 mph. Are you following along or did I blow you away?

Now, the problem tells us that at 4 pm, the average wind speed was at least 32 mph. So we can write the inequality:

(x + 19) - 5 ≥ 32

Alright, let's solve this gusty equation:

(x + 14) ≥ 32

Subtract 14 from both sides to isolate the x:

x ≥ 18

So, the minimum value of the average wind speed at 8 am is 18 miles per hour. Don't let that breeze ruffle your feathers!

To solve the problem, let's denote the average wind speed at 8 AM as "x."

From 8 AM to 12 noon, the wind speed increased by 19 miles/h, so at 12 noon the average wind speed would be x + 19 miles/h.

From 12 noon to 4 PM, the wind speed decreased by 5 miles/h, so at 4 PM the average wind speed would be (x + 19) - 5 miles/h, which simplifies to x + 14 miles/h.

According to the problem, at 4 PM the average wind speed was at least 32 miles/h, so we can write the inequality:

x + 14 ≥ 32

Now, we can solve the inequality for x:

x + 14 ≥ 32
x ≥ 32 - 14
x ≥ 18

Therefore, the minimum value of the average wind speed at 8 AM is 18 miles/h.

X>1243