Question

What is the value of x in the equation (3x+5)/2=(5x+3)/3

Answer 1

`x = 9`

Explanation:

`(3x + 5)/(2) = 1 + (5x)/(3) \\ 3(3x + 5) = 6 + 10x \\ 9x + 15 = 6 + 10x \\ 15 = 6 + 10x - 9 \\ 15 = 6 + x \\ 15 - 6 = x \\ 9 = x \\ x = 9`

Answer 2

x = 9

Explanation:

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

multiply both sides by 6 ( the LCM of 2 and 3 ) to clear the fractions

3(3x + 5) = 2(5x + 3) ← distribute parenthesis

9x + 15 = 10x + 6 ( subtract 9x from both sides )

15 = x + 6 ( subtract 6 from both sides )

9 = x