How do you solve $5root3(4x-1)+2=17$ ?

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Answer 1 · 2016-06-01T06:43:32

$x=7$

$5xxroot(3)(4x-1)+2=17$

Here, we try to keep the cube root term on one side.

Subtract $2$ from both sides:

$5xxroot(3)(4x-1)+2color(red)(-2)=17color(red)(-2)$

$5xxroot(3)(4x-1)=15$

Next, divide both sides by $5$ :

$[5xxroot(3)(4x-1)]/color(red)(5)=15/color(red)(5)$

$root(3)(4x-1)=3$

Now, we remove the cube root.
In order to do so, find the cube of both sides:

$(root(3)(4x-1))^color(red)(3)=3^color(red)(3)$

$4x-1=3xx3xx3$

$4x-1=27$

$4x-1color(red)(+1)=27color(red)(+1)$

$4x=28$

$(4x)/color(red)(4)=28/color(red)(4)$

$x=7$

How do you solve 5root3(4x-1)+2=175root3(4x-1)+2=17?