Question

radical equations quick check
solve (sqrt5{5x - 3} = 2) and choose the correct value. (1 point)
( circ ) ( x = -\frac{29}{5} )
( circ ) ( x = \frac{4}{5} )
( circ ) ( x = \frac{3}{5} )
( circ ) ( x = 7 )

Explanation:

Step1: Eliminate the fifth root

To solve the equation \(\sqrt[5]{5x - 3}=2\), we raise both sides to the power of 5. This is because \((\sqrt[n]{a})^n=a\) for any real number \(a\) and positive integer \(n\). So, we have \((\sqrt[5]{5x - 3})^5 = 2^5\).
Simplifying both sides, the left - hand side becomes \(5x-3\) and the right - hand side is \(32\) (since \(2^5=2\times2\times2\times2\times2 = 32\)). So the equation simplifies to \(5x - 3=32\).

Step2: Solve for \(x\)

We add 3 to both sides of the equation \(5x - 3 = 32\) to isolate the term with \(x\). Using the addition property of equality (if \(a=b\), then \(a + c=b + c\)), we get \(5x-3 + 3=32 + 3\), which simplifies to \(5x=35\).
Then, we divide both sides of the equation \(5x = 35\) by 5. Using the division property of equality (if \(a=b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)), we have \(\frac{5x}{5}=\frac{35}{5}\), so \(x = 7\).

Answer:

\(x = 7\) (the option " \(x = 7\)")