Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10.

Solution:

Given: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10

Expression is 1/2 + (4/2x) = (x + 4)/10

Taking LCM

⇒ (x/2x) + (4/2x) = (x + 4)/10

⇒ (x + 4)/2x = (x + 4)/10

By cross multiplication,

⇒ 10(x + 4) = 2x(x + 4)

So we get, 

⇒ 10x + 40 = 2x² + 8x

On grouping,

⇒ 2x² - 2x = 40

Divide both sides by 2

⇒ x² - x = 20

⇒ x² - x - 20 = 0

On simplification, we get

(x - 5)(x + 4) = 0

x = 5 or -4

Therefore, the value of x is 5 or -4.

---

Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10.

Summary:

The value of x if 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10 is 5 or -4.