Answer:[tex]x<3[/tex] Step-by-step explanation:[tex]\frac{1}{3}(3x-6)^3+4<13[/tex]Solving the inequality to have solutions for [tex]x[/tex]Subtracting 4 from both sides.⇒ [tex]\frac{1}{3}(3x-6)^3+4-4<13-4[/tex]⇒ [tex]\frac{1}{3}(3x-6)^3<9[/tex]Multiplying 3 both sides to remove fraction.⇒ [tex]3\times \frac{1}{3}(3x-6)^3<9\times 3[/tex]⇒ [tex](3x-6)^3<27[/tex]Taking cube root both sides to remove the cube.⇒ [tex]\sqrt[3]{(3x-6)^3}<\sqrt[3]{27}[/tex]⇒ [tex](3x-6)<3[/tex] [ ∵ [tex]\sqrt[3]{27} =3[/tex] ]Adding 6 to both sides.⇒ [tex]3x-6+6<3+6[/tex] ⇒ [tex]3x<9[/tex] Dividing both sides by [tex]3[/tex]⇒ [tex]\frac{3x}{3}<\frac{9}{3}[/tex] ∴ [tex]x<3[/tex]