Question

Solve for x: 4 over 5 x + 4 over 3 = 2x x = Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. (2 points)

Answer 1

(5 + √115)/15 or (5 - √115)/15

Explanation:

4/5x+4/3 = 2x

Multiply each term by the least common multiple of the denominators (15x)

12 + 20x = 30x²

Move all the terms to the left-hand side.

-30x² + 20x + 12 = 0

Multiply each term by -1

30x² - 20x - 12 = 0

Remove the common factor (2)

15x² - 10x - 6 = 0

Solve by using the quadratic formula

a = 15, b = -10, c = -6

`x = (-b\pm√(b^2-4ac))/(2a)\\\\= (-(-10)\pm√((-10)^2-4(15)(-6)))/(2(15))\\\\= (10\pm√(100 + 360))/(30)\\\\= (10\pm√(460))/(30)\\\\= (10\pm√(4*115))/(30)\\\\= (10\pm2√(115))/(30)\\\\= \mathbf{(5\pm√(115))/(15)}`

x = (5 + √115)/15 or x = (5 - √115)/15