# 6/3x−4>x+1

$\frac{6}{3x-4}>x+1$
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Multiply both sides of the inequality by 3x−4:
$6>\left(x+1\right)\left(3x-4\right)$
Distribute the right-side: $6>\left(3{x}^{2}-4x+3x-4\right)$
Simplify by adding like terms and subtract the 6 from both sides:
$6-6>3{x}^{2}-x-4-6$
$0>3{x}^{2}-x-10$
Factor the right-side: 0>(3x+5)(x−2) or (3x+5)(x−2)<0
Solve for values of x that make the equation negative:
3x+5<0 and x−2<0
3x<−5 and x<2
$x<-\frac{5}{3}$
Therefore: $-\frac{5}{3}