Solve for x: 4/5 x + 4/3 = 2x

X=?

x = 10/9

Step-by-step explanation:

Solve for x:

(4 x) / 5 + 4/3 = 2 x

Put each term in (4 x) / 5 + 4/3 over the common denominator 15: (4 x) / 5 + 4/3 = (12 x) / 15 + 20/15:

(12 x) / 15 + 20/15 = 2 x

(12 x) / 15 + 20/15 = (12 x + 20) / 15:

(12 x + 20) / 15 = 2 x

Multiply both sides by 15:

(15 (12 x + 20)) / 15 = 15*2 x

(15 (12 x + 20)) / 15 = 15/15 * (12 x + 20) = 12 x + 20:

12 x + 20 = 15*2 x

15*2 = 30:

12 x + 20 = 30 x

Subtract 30 x from both sides:

(12 x - 30 x) + 20 = 30 x - 30 x

12 x - 30 x = - 18 x:

-18 x + 20 = 30 x - 30 x

30 x - 30 x = 0:

20 - 18 x = 0

Subtract 20 from both sides:

(20 - 20) - 18 x = - 20

20 - 20 = 0:

-18 x = - 20

Divide both sides of - 18 x = - 20 by - 18:

(-18 x) / (-18) = (-20) / (-18)

(-18) / (-18) = 1:

x = (-20) / (-18)

The gcd of 20 and - 18 is 2, so (-20) / (-18) = ( - (2*10)) / (2 (-9)) = 2/2 * (-10) / (-9) = (-10) / (-9):

x = (-10) / (-9)

Multiply numerator and denominator of (-10) / (-9) by - 1:

Answer: x = 10/9