Question

HELP DUE IN 10 MINS!

Solve for x.

5 / 4x - 6 = 2 / x - 9

Answer 1

`\\ \sf\longmapsto (5)/(4x-6)=(2)/(x-9)`

`\\ \sf\longmapsto 5(x-9)=2(4x-6)`

`\\ \sf\longmapsto 5x-45=8x-12`

`\\ \sf\longmapsto 5x-8x=-12+45`

`\\ \sf\longmapsto -3x=33`

`\\ \sf\longmapsto x=(33)/(-3)`

`\\ \sf\longmapsto x=-11`

Answer 2

`\huge \boxed{\mathfrak{Question} \downarrow}`

`\large \sf \: \frac { 5 } { 4 x - 6 } = \frac { 2 } { x - 9}, \: Solve \: for \: x\\`

`\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}`

`\large \sf\frac { 5 } { 4 x - 6} = \frac { 2 } { x - 9} \\`

Variable x cannot be equal to any of the values
`\sf(3)/(2)`,9 as division by zero is not defined. Multiply both sides of the equation by
`\sf2\left(x-9\right)\left(2x-3\right)`, the least common multiple of 4x-6 ,x-9.

`\large \sf\left(x-9\right)* 5=\left(4x-6\right)* 2`

Use the distributive property to multiply x-9 by 5.

`\large \sf5x-45=8x-12`

Subtract 8x from both sides.

`\large \sf5x-45-8x=-12`

Combine 5x and -8x to get -3x.

`\large \sf-3x-45=-12`

Add 45 to both sides.

`\large \sf \: -3x=-12+45`

Add -12 and 45 to get 33.

`\large \sf-3x=33`

Divide both sides by -3.

`\large \sf x=(33)/(-3) \\`

Divide 33 by -3 to get -11.

`\large\boxed{\boxed{ \boxed{ \mathfrak{x= - 11}}}}`