Solve ^5√5x−3=2

Question

and choose the correct value.(1 point)
Responses

x=35
x equals Start Fraction 3 over 5 End Fraction

x=45
x equals Start Fraction 4 over 5 End Fraction

x=7
x equals 7

x=−295
x equals negative Start Fraction 29 over 5 End Fraction
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Answer 1

To solve the equation \( \sqrt[5]{5x - 3} = 2 \), we start by eliminating the fifth root.

1. Raise both sides to the power of 5 to get rid of the root: \[ 5x - 3 = 2^5 \]

2. Calculate \( 2^5 \): \[ 2^5 = 32 \] Now the equation looks like this: \[ 5x - 3 = 32 \]

3. Add 3 to both sides: \[ 5x = 32 + 3 \] \[ 5x = 35 \]

4. Finally, divide by 5 to solve for \( x \): \[ x = \frac{35}{5} \] \[ x = 7 \]

Thus, the solution to the equation is \( x = 7 \).

The correct response is: x = 7.