Answer {x:x<10/3}
step by step explanation
first you need to change the less than sign to equal to sign
thus
[tex] \frac{x - 2}{x - 3} = 4[/tex]
cross multiplying
[tex]x - 2 = 4(x - 3)[/tex]
[tex]x - 2 = 4x - 12[/tex]
grouping of like terms
[tex]4x - x = - 2 + 12[/tex]
[tex]3x = 10[/tex]
dividing through by 3
[tex] \frac{3x}{3} = \frac{10}{3} [/tex]
[tex]x = \frac{10}{3} [/tex]
now the truth set is
{x:x<10/3}
the < did not change because we didn't divide by a negative number when finding for the x.
