Question

homework 10: section 2.6
score: 30/180 answered: 3/18
question 4
solve for ( x ).
( sqrt5{4x - 9} = 2 )
( x = )
question help: message instructor

Explanation:

Step1: Raise both sides to the 5th power

To eliminate the fifth root, we raise both sides of the equation \(\sqrt[5]{4x - 9}=2\) to the 5th power. By the property of exponents, \((\sqrt[n]{a})^n=a\) for any real number \(a\) (when \(n\) is odd, which it is here, \(n = 5\)). So we have \((\sqrt[5]{4x - 9})^5=2^5\).
Simplifying both sides, the left - hand side becomes \(4x-9\) and the right - hand side is \(32\) (since \(2^5=32\)). So the equation is now \(4x - 9=32\).

Step2: Solve for x

We want to isolate \(x\). First, add 9 to both sides of the equation \(4x - 9=32\).
Adding 9 to both sides: \(4x-9 + 9=32 + 9\).
Simplifying, we get \(4x=41\).
Then, divide both sides by 4: \(x=\frac{41}{4}\) (or \(x = 10.25\)).

Answer:

\(\frac{41}{4}\) (or \(10.25\))