Answer:
a. 10 = 1+7x/7+x
Multiplying both sides of the equation by 7+x, we get:
10(7+x) = (1+7x)(7+x)
70+10x = 7+7x+x+7x^2
9x^2+17x-70 = 0
This is a quadratic equation, which means that it has two solutions. We can find these solutions using the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-17 +/- sqrt(289 - 4(9)(-70))) / (2(9))
x = (-17 +/- sqrt(289 + 2520)) / 18
x = (-17 +/- sqrt(2809)) / 18
x = (-17 +/- 53.1) / 18
x = (-70 +/- 53.1) / 18
x = (-16.9, 36.9)
b. 0.2 = 6+2x/12+r
Multiplying both sides of the equation by 12+r, we get:
0.2(12+r) = (6+2x)(12+r)
2.4+0.2r = 72+12r+2xr
0.2r - 2xr = 72 - 2.4
-2xr = 72 - 2.4 - 0.2r
-2xr = 72 - 2.6 - r
-2xr - r = 72 - 2.6 - r
-3xr = 69.4
xr = -23.1
x = -23.1 / r
c. 0.8= x/0.5+x
Multiplying both sides of the equation by 0.5, we get:
0.8*0.5 = (x/0.5+x)(0.5)
0.4 = x+x^2
x^2 + x - 0.4 = 0
This is a quadratic equation, which means that it has two solutions. We can find these solutions using the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-1 +/- sqrt(1 - 4(-0.4)) / (2(1))
x = (-1 +/- sqrt(1 + 1.6)) / 2
x = (-1 +/- sqrt(2.6)) / 2
x = (-1 +/- 1.61) / 2
x = (-2.61, 0.61)
d. 3.5 =4+2x/0.5-x
Multiplying both sides of the equation by 0.5, we get:
3.5*0.5 = (4+2x)(0.5) - x(0.5)
1.75 = 2 + x - 0.5x
1.75 = 2 - 0.5x + x
1.75 = 2
This equation is not true, so there are no values of x that make it true.
Hopefully I'm right
Explanation: