Question

solve for x : 1/2a+b+2x = 1/2a +1/b+ 1/2x

Answer 1

1/(2a + b + 2x) = 1/2a + 1/b + 1/2x

or, 1/(2a + b + 2x) - 1/2a = 1/b + 1/2x

or, (2a -2a - b - 2x)/(2a + b + 2x)2a = 1/b + 1/2x

or, -(b + 2x)/(2a + b + 2x)2a = (2x + b)/2xb

[ taking (b + 2x) from both sides so, one solution is from b +2x = 0 , x = -b/2 ]

or, -1/(2a + b + 2x)2a = 1/2xb

or, -2xb = (2a + b + 2x)2a

or, -xb = (2a + b + 2x)a

or, -xb = 2a² + ab + 2xa

or, 2a² + ab + 2xa + xb = 0

or, a(2a + b) + x(2a + b) = p

or, (x + a)(2a + b) = 0

or, x + a = 0 => x = -a

hence, x = -a and -b/2

Answer 2

Answer:

x=$\frac{2}{b}$   or x = 1-b²

Step-by-step explanation:

Given Equation is

$\frac{1}{2}a + b + 2x = \frac{1}{2}a + \frac{1}{b} + \frac{1}{2}x$

Now subtracting \frac{1}{2}a from both sides of the equation

$\frac{1}{2}a + b + 2x - \frac{1}{2}a = \frac{1}{2}a + \frac{1}{b} + \frac{1}{2}x - \frac{1}{2}a$

$b + 2x = \frac{1}{b} + \frac{1}{2}x$

Subtratcing b and  from both sides $\frac{1}{2}x$ from both sides

$2x-\frac{1}{2}x=\frac{1}{b}-b$

$\frac{1}{2}x=\frac{1-b²}{b}$

Multiplying both sides by 2

  $x=\frac{2}{b}(1-(b)²)$

x= $\frac{2}{b}$                         or x= 1-b²