Solve the inequality $10

Question

Solve the inequality $10 < x ^ { 3 } - 1 < 26$ Restrict your attention to positive values of $x$ . 
A) $\quad 3.97 < x < 3$
B) $2.22 < x < 3$
C) $2.22 < x < 7.98$
D) $\quad 3.97 < x < 7.98$

Quizplus · Accepted Answer

To solve the inequality $10 < x^3 - 1 < 26$, we first solve for $x^3$ in both cases: $10 + 1 < x^3 < 26 + 1$, which simplifies to $11 < x^3 < 27$. Taking the cube root of all sides gives us $2.22 < x < 3$, since $\sqrt[3]{11} \approx 2.22$ and $\sqrt[3]{27} = 3$. This restricts $x$ to positive values between 2.22 and 3.

Solve the Inequality 10<x3−1<2610 < x ^ { 3 } - 1 < 2610<x3−1<26

Solve the Inequality $10 < x ^ { 3 } - 1 < 26$