Question

What is
1/3(3x-6)^3+4<13​

Answer 1

`x<3`

Explanation:

`(1)/(3)(3x-6)^3+4<13`

Solving the inequality to have solutions for
`x`

Subtracting 4 from both sides.

⇒
`(1)/(3)(3x-6)^3+4-4<13-4`

⇒
`(1)/(3)(3x-6)^3<9`

Multiplying 3 both sides to remove fraction.

⇒
`3* (1)/(3)(3x-6)^3<9* 3`

⇒
`(3x-6)^3<27`

Taking cube root both sides to remove the cube.

⇒
`\sqrt[3]{(3x-6)^3}<\sqrt[3]{27}`

⇒
`(3x-6)<3` [ ∵
`\sqrt[3]{27} =3` ]

Adding 6 to both sides.

⇒
`3x-6+6<3+6`

⇒
`3x<9`

Dividing both sides by
`3`

⇒
`(3x)/(3)<(9)/(3)`

∴
`x<3`