Question

1/2+4/2x=x+4/10
solve for x

Answer 1

First, get rid of the denominator on the right side of the equal sign by multiplying through by 10 to get:
5+20x=x+4
then simplify by adding the like terms and computing the value of x.

Answer 2

\(\large\frac{1}{2} + \frac{4}{2x} = \frac{x+4}{10} \)

Multiply the first fraction by x/x :

\(\large\frac{x}{2x} + \frac{4}{2x} = \frac{x+4}{10} \)

Combine the fractions on the left side to get

\(\large\frac{x+4}{2x} = \frac{x+4}{10} \)


Cross multiply to get:

2x(x+4) = 10(x+4)

\(2x^2 + 8x = 10x + 40 \\ 2x^2 - 2x - 40 = 0 \\ 2(x^2 - x - 20) = 0 \\ x^2 - x - 20 = 0 \\ x^2 - 5x + 4x - 20 = 0 \\ x(x-5) + 4(x-5) = 0 \\ (x-5)(x+4) = 0 \\ x = 5, x = -4\)

Answer 3

Nice.