Question

6 x minus 3 / 2 X + 7 is equals to 3 x minus 2 divided by X + 5 .
Please solve it.
​

Answer 1

x =
`(1)/(10)`

Step-by-step explanation:

`(6x-3)/(2x+7)` =
`(3x-2)/(x+5)` ( cross- multiply )

(3x - 2)(2x + 7) = (6x - 3)(x + 5) ← expand factors on both sides using foil

6x² + 17x - 14 = 6x² + 27x - 15 ( subtract 6x² from both sides )

17x - 14 = 27x - 15 ( subtract 27x from both sides )

- 10x - 14 = - 15 ( add 14 to both sides )

- 10x = - 1 ( divide both sides by - 10 )

x =
`(-1)/(-10)` =
`(1)/(10)`

Answer 2

x = 0.1

Step-by-step explanation:

`\sf \rightarrow (6x-3)/(2x+7) = (3x-2)/(x+5)`

cross multiply

`\sf \rightarrow (6x-3)(x+5) = (3x-2)(2x+7)`

distribute

`\sf \rightarrow 6x^2 + 30x - 3x - 15 = 6x^2 + 21x - 4x - 14`

simplify

`\sf \rightarrow 6x^2 + 27x - 15 = 6x^2 + 17x- 14`

collect terms

`\sf \rightarrow 6x^2 + 27x - 15 - 6x^2 - 17x + 14=0`

simplify

`\sf \rightarrow 10x- 1=0`

isolate

`\sf \rightarrow 10x=1`

divide

`\sf \rightarrow x=1/10 \qquad or \qquad 0.1`