4x + 6 < -6
subtract 6 from each side
4x < -12
divide by 4
x < -3
- 2/5 x-9 < 9/10
multiply each side by 10 to get rid of the fractions
10*(- 2/5 x-9) < 10*9/10
distribute
-4x -90 <9
add 90 to each side
-4x < 99
divide by -4 (which flips the inequality)
x> -99/4
x> -24 3/4
First we'll consider the floor size.
In a 10 by 12 room the longest pipe that will fit lying on the floor equals the hypotenuse of a 10 by 12 triangle:
hypotenuse² = 10² + 12²
hypotenuse² = 100 + 144
hypotenuse² = 244
hypotenuse =
<span>
<span>
<span>
15.62 feet
Now we have to consider the third dimension (height = 8 feet).
The two sides would be 15.62 and 8
</span></span></span>hypotenuse² =
15.62² + 8²
hypotenuse² =
244 + 64 = 308
hypotenuse = 17.55
So, the longest pipe that would fit in that room would be 17.55 feet long.
