Question

homework 10: section 2.6
score: 0/180 answered: 0/18
question 3
solve for x. \\(\sqrt5{4x - 3} = 3\\)
x =
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Explanation:

Step1: Eliminate the fifth root

To solve for \( x \) in the equation \( \sqrt[5]{4x - 3}=3 \), we raise both sides of the equation to the power of 5 to eliminate the fifth root. Recall that \( (\sqrt[n]{a})^n=a \) for any real number \( a \) and positive integer \( n \). So we have:
\[
(\sqrt[5]{4x - 3})^5 = 3^5
\]
Simplifying both sides, the left - hand side becomes \( 4x-3 \) and the right - hand side is \( 3^5 = 243 \). So the equation simplifies to:
\[
4x-3=243
\]

Step2: Solve for \( x \)

Now we solve the linear equation \( 4x - 3=243 \) for \( x \). First, we add 3 to both sides of the equation to isolate the term with \( x \):
\[
4x-3 + 3=243+3
\]
Simplifying both sides, we get \( 4x=246 \). Then, we divide both sides by 4:
\[
x=\frac{246}{4}=\frac{123}{2} = 61.5
\]

Answer:

\( x=\frac{123}{2} \) (or \( x = 61.5 \))