What are the solutions for x in the proportion 5 times x minus 6 all over x equals 2 times x all over 2?

Answer 1

(5x - 6) 2x

------- = --

x . 2

Tried to show it how you'd write it, but it doesn't look so well: (5x - 6) / x = 2x / 2

First of all, x cannot equal zero. So multiply both sides by x and simplify:

5x - 6 = x² ---> x² - 5x + 6 = 0 : (x - 2)(x - 3) = 0, so the two solutions are x = {2, 3}

Check in original equation: (5*2 - 6)/2 = 4/2 =2. 2*2 / 2 = 2 . check

(5*3 - 6)/3 = 9/3 =3. 2*3 / 2 = 3. check