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]
