how do you solve for x in the following problem? 2/x= x/3 + x/8 + x/2?

Answer 1

2/x = x/3 + x/8 + x/2

The LCD is 24x, so multiply 24x to both sides.
48 = 8x² + 3x² + 12x²

Simplify,
48 = 23x²

Divide by 23
x² = 48/23

then get the square root of both sides,
x = ±√(48/23)

Rationalize the denominator, and simplify the radical
x = ±4/23 √3

Therefore, the solutions for x are:
x = 4/23 √3 and
x = -4/23 √3

^_^

Answer 2

Multiply both sides by 24x:
24x(2/x)=24x(x/3+x/8+x/2)
48=8x^2+3x^2+12x^2
23x^2=48
x^2=48/23
√x^2=±√48/23
x=±√48/23

Answer 3

2/x= x/3 + x/8 + x/2 LCD is 24

2/x = (x/3 + x/8 + x/2)(24/24)

2/x = 23x/24 multiply both sides by 24

48/x = 23x multiply both sides by x

48 = 23x^2 divide both sides by 23

48/23 = x^2 To get x by its self take the square root of both sides

√(48/23) = √(x^2)
± √(48/23) = x

x = ± (4*√ 69)/23

NOTE: Don’t forget that when you take the square root of a term there are two answers.

Answer 4

2/x = x/3 + x/8 + x/2
multiply throught by 24x..
48 = 8x^2 + 3x^2 + 12x^2
48 = 23x^2
x^2 = 48/23
x = sq root (48/23)

Answer 5

x/3 + x/8 + x/2 = 8x/24 + 3x/24 + 12x/24 = 23x/24.

23x/24 = 2/x

23x^2/24 = 2

23x^2 = 48

x^2 = 48/23

x = sqrt(48/23)

Answer 6

(24)(2/x)= (x/3+x/8+x/2)(24)
48/x=8x+3x+12x--now you cross multiply...
48=23x^2 x^2 means x squared.
x^2=48/23
x=+-sqrt(48/23)

Answer 7

2/x = 8x + 3x + 12x/ common denominator 24
x = 8x + 3x + 12x/ 24 X 2
x = 16x + 6x + 24x /24
x = 46x/24
x = 23x/24

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