[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \large \sf \: \frac { 5 } { 4 x - 6 } = \frac { 2 } { x - 9}, \: Solve \: for \: x\\ [/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \large \sf\frac { 5 } { 4 x - 6} = \frac { 2 } { x - 9} \\ [/tex]
Variable x cannot be equal to any of the values [tex]\sf\frac{3}{2}[/tex],9 as division by zero is not defined. Multiply both sides of the equation by [tex]\sf2\left(x-9\right)\left(2x-3\right)[/tex], the least common multiple of 4x-6 ,x-9.
[tex] \large \sf\left(x-9\right)\times 5=\left(4x-6\right)\times 2 [/tex]
Use the distributive property to multiply x-9 by 5.
[tex] \large \sf5x-45=8x-12 [/tex]
Subtract 8x from both sides.
[tex] \large \sf5x-45-8x=-12 [/tex]
Combine 5x and -8x to get -3x.
[tex] \large \sf-3x-45=-12 [/tex]
Add 45 to both sides.
[tex] \large \sf \: -3x=-12+45 [/tex]
Add -12 and 45 to get 33.
[tex] \large \sf-3x=33 [/tex]
Divide both sides by -3.
[tex] \large \sf x=\frac{33}{-3} \\ [/tex]
Divide 33 by -3 to get -11.
[tex]\large\boxed{\boxed{ \boxed{ \mathfrak{x= - 11}}}}[/tex]
