algebra...HELP!?

Question

I've got 3/4 of the assignment done but these ones are killing me. Any help would be greatly appreciated!
21. solve: 8x/7 - 5 = 6x/7-1

31. An airplane covered 23 miles of its route while dcreasing it's altitude by 19000 feet. Find the slope of the arplane's line of decscent.

33. Write the equation of the line that passes therought the point (-2,10) with a slope of -4.

40. A home-based company produces both hand kintted scarces and sweaters. The scarve take 2 hours of labor to producae and the sweaters take 14 hours. The labor available is limited to 40 hours per week and the total production capacity is 5 items per week. Write a system of inequalites representing this situation where x is the number of scarves and y is the number of sweaters.


THANK YOU!

Answer 1

21: multiply through by 7, and you get
8x - 35 = 6x - 7

Subtract 6x from both sides, you get 2x - 35 = -7
So
2x = 28, and x = 14.

31. Slope = rise/run = -19000/23

33. Using point-slope form: y - 10 = -4(x+2)
So
y-10 = -4x - 8, then y = -4x + 2 is the answer in slope-intercept form.

40. 2x + 14y <= 40
x+y <= 5

***Note, most of you are missing the fact that the plane's altitude is DECREASING on #31, so the slope is negative!

Answer 2

1 x=2

Answer 3

21. (8x/7-5)7=(6x/7-1)7 multiply both sides by 7 to eliminate the denominatore

8x-35*=6x-7*
8x-6x=-7+35 combine like terms
2x=28 divide both sides by two
x=14
* 35 and 7 came from -5*7 and -1*7

33. x: -2 y: 10 m:-4
y=mx+b--point slope form formula
substitute the formula

10=-4(-2)+b
10=8+b
b=2
y=-4x+2---equation

40. 2x+14y<=40
x+y<=5
*<=...is greater than or equal to

don't know how to solve the other one i don't like solving those kind of problems ^_^ goodluck

Answer 4

2x/7 = 4 --> 2x = 28 --> x = 14

slope = 19000/(23*5280) = 0.156455863

y = -4x +b
10 = -4(-2) +b --> b = 18
So y = -4x+18

x= scarf and y = sweater
2x + 14y =< 40
x+y=<5

Answer 5

21. x=0 by cross muli.

33. y= - 4x + 2

Answer 6

31. -19000/23