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For each equation below, find the value(s) of x that make it true.

a. 10 = 1+7x/7+x
b. 0.2 =6+2x/12+r
c. 0.8= x/0.5+x
d. 3.5 =4+2x/0.5-x

User Ghis
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1 Answer

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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:

User Imcoddy
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