What is the solution to the equation 1/2x+1/5x=1/6x−1/6?

1/2 x + 1/5 x = 1/6 x - 1/6

first you have to find the common denominator which is 30

15/30 x + 6/30 x = 5/30 x - 5/30

21/30 x = 5 /30 x-5/30

subtract 5/30 from each side

16/30 x =- 5/30

 multiply each side by 30

16 x = -5

divide each side by 16

x = -5/16

fwms@lil_ben06

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240