Question

HELP DUE IN 10 MINS! Solve for x. 5 / 4x - 6 = 2 / x - 9

Answer 1

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

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

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

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

Variable x cannot be equal to any of the values $\sf\frac{3}{2}$,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.

$\large \sf\left(x-9\right)\times 5=\left(4x-6\right)\times 2$

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.

$\large \sf x=\frac{33}{-3}$

Divide 33 by -3 to get -11.

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

Answer 2

$\\ \sf\longmapsto \dfrac{5}{4x-6}=\dfrac{2}{x-9}$

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

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

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

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

$\\ \sf\longmapsto x=\dfrac{33}{-3}$

$\\ \sf\longmapsto x=-11$