Solve u_n(1-u_{n 1})>1/4

Evaluate

u_{n} (1 - u) > \frac{1}{4}

Calculate

\frac{4 u _{n} - 4 u _{n} u - 1}{4} > 0

Rewrite the expression

4 u_{n} - 4 u_{n} u - 1 > 0

Simplify

4 u_{n} - 1 - 4 u_{n} u > 0

Move the constant to the right side

- 4 u_{n} u > 0 - (4 u_{n} - 1)

Subtract the terms

More Steps

- 4 u_{n} u > - 4 u_{n} + 1

Divide both sides

\frac{- 4 u _{n} u}{- 4 u _{n}} > \frac{- 4 u _{n} + 1}{- 4 u _{n}}

Divide the numbers

u > \frac{- 4 u _{n} + 1}{- 4 u _{n}}

Divide the numbers

More Steps

u > \frac{4 u _{n} - 1}{4 u _{n}}

Rewrite the inequalities

{u > \frac{4 u _{n} - 1}{4 u _{n}} - u_{n} > 0 {u < \frac{4 u _{n} - 1}{4 u _{n}} - u_{n} < 0

Change the signs on both sides of the inequality and flip the inequality sign

{u > \frac{4 u _{n} - 1}{4 u _{n}} u_{n} < 0 {u < \frac{4 u _{n} - 1}{4 u _{n}} - u_{n} < 0

Change the signs on both sides of the inequality and flip the inequality sign

{u > \frac{4 u _{n} - 1}{4 u _{n}} u_{n} < 0 {u < \frac{4 u _{n} - 1}{4 u _{n}} u_{n} > 0

Solution

u > \frac{4 u _{n} - 1}{4 u _{n}}, u_{n} < 0 u < \frac{4 u _{n} - 1}{4 u _{n}}, u_{n} > 0

Solve the inequality