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

Question

Kennedy Adams · Accepted Answer

#x=7#

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

This is an attempt to maintain 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#

The cube of both sides must be found in order to remove the cube root, which we do now:

#(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#

Avery Alexander · Answer

undefined To solve the equation 5√3(4x-1)+2=17, we can follow these steps:

1. Subtract 2 from both sides of the equation: 5√3(4x-1) = 15.
2. Divide both sides of the equation by 5√3: 4x-1 = 3.
3. Add 1 to both sides of the equation: 4x = 4.
4. Divide both sides of the equation by 4: x = 1.

Therefore, the solution to the equation is x = 1.