Question Solve x1/3<4/5.(1 point) Responses x>525 x greater than Start Fraction 52 over 5 End Fraction x<1345 x less than 13 Start Fraction 4 over 5 End Fraction x<465 x less than Start Fraction 4 over 65 End Fraction x<1025
To solve the inequality \( x^{\frac{1}{3}} < \frac{4}{5} \), we need to find the range of values for x that, when the cube root is taken, results in a number less than \(\frac{4}{5}\).
First, let's isolate x by raising both sides to the power of 3 to get rid of the cube root:
\( (x^{\frac{1}{3}})^3 < (\frac{4}{5})^3 \)
When we raise both sides to the power of 3, we get:
\( x < (\frac{4}{5})^3 \)
Now calculate the cube of \(\frac{4}{5}\):
\( (\frac{4}{5})^3 = \frac{4^3}{5^3} = \frac{64}{125} \)
Thus the inequality becomes:
\( x < \frac{64}{125} \)
None of the options you provided exactly correspond to this result, but from the information given, it looks like there might be a typographical error. The correct range of values for x is all numbers less than \(\frac{64}{125}\). If we compare this with the options you've provided, the closest (but not correct) would be:
\( x < \frac{4}{65} \)
However, this is not the right answer. The correct inequality based on your options format should look like:
\( x < \frac{64}{125} \)