How to solve this inequality involving a 4th root?

[PhizKid]

Homework Statement

$$\sqrt[4]{2x + 1} - 0.1 < \frac{1}{2}x + 1 < \sqrt[4]{2x + 1} + 0.1$$

Homework Equations

The Attempt at a Solution

I'm having trouble getting just an 'x' by itself in the middle because of the 4th root. How should I solve this inequality? I tried everything but always end up with something to the 4th power after expanding 4 binomials.

(Solution: -0.368935 < x < 0.677669)

 

[LCKurtz]

Homework Statement

$$\sqrt[4]{2x + 1} - 0.1 < \frac{1}{2}x + 1 < \sqrt[4]{2x + 1} + 0.1$$

I'm having trouble getting just an 'x' by itself in the middle because of the 4th root. How should I solve this inequality? I tried everything but always end up with something to the 4th power after expanding 4 binomials.

(Solution: -0.368935 < x < 0.677669)

I would think about expanding $\sqrt[4]{1+2x}$ as a binomial or Taylor series with error estimates.

 

[ehild]

Try to solve the inequalities separately.

$$\sqrt[4]{2x + 1} < \frac{1}{2}x + 1.1$$
$$\sqrt[4]{2x + 1} > \frac{1}{2}x + 0.9$$

ehild