Question

How do you solve `7- ( 3x + 29 )^(1/4) = 3`?

Answer 1

`x=75 2/3~~75.bar6`

Explanation:

`color(blue)(7-(3x+29)^(1/4)=3`

We need to isolate `x`

Subtract `7` both sides

`rarr7-(3x+29)^(1/4)-color(red)(7)=3-color(red)(7)`

`rarr-(3x+29)^(1/4)=-4`

Multiply both sides by `-1` to make the left side positive

`rarr-(3x+29)^(1/4)*color(red)((-1))=-4*color(red)((-1))`

`rarr(3x+29)^(1/4)=4`

We use the formula

`color(red)(x^(z/y)=root(y)(x^z)`

So,

`color(red)((3x+29)^(1/4)=root(4)(3x+29)^1=root(4)(3x+29)`

`rarrroot(4)(3x+29)=4`

To get rid of the root sign,raise both sides to the power of `4`

`rarr(root(4)(3x+29))^4=4^4`

`rarr3x+29=256`

Subtract `29` both sides

`rarr3x+29-color(red)(29)=256-color(red)(29)`

`rarr3x=227`

Divide both sides by `3`

`rarr(3x)/(color(red)(3))=227/(color(red)(3))`

`color(green)(rArrx=227/3=75 2/3`