Solve the inequality $7

Question

Solve the inequality $7 < x ^ { 3 } - 1 < 26$ . Restrict your attention to positive values of $x$ . 
A) $\quad 3.16 < x < 3$
B) $2 < x < 3$
C) $2 < x < 7.9$
D) $3.16 < x < 7.9$ $$\sqrt { x } + \sqrt { x + 1 } > x + 1$$

Quizplus · Accepted Answer

To solve the inequality $7 < x^3 - 1 < 26$, we first add 1 to all parts of the inequality to get $8 < x^3 < 27$. Taking the cube root of all parts gives $2 < x < 3$, since the cube root of 8 is 2 and the cube root of 27 is 3. This solution is restricted to positive values of $x$, which fits the given range.

Solve the Inequality 7<x3−1<267 < x ^ { 3 } - 1 < 267<x3−1<26

Solve the Inequality $7 < x ^ { 3 } - 1 < 26$