en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2+1>4x

Solution

4 x^{2} + 1 > 4 x

Solution

x < \frac{1}{2} or x > \frac{1}{2}

+2

Interval Notation

(- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Decimal Notation

x < 0.5 or x > 0.5

Solution steps

4 x^{2} + 1 > 4 x

Rewrite in standard form

4 x^{2} + 1 - 4 x > 0

Factor

4 x^{2} + 1 - 4 x : (2 x - 1)^{2}

(2 x - 1)^{2} > 0

For

u^{n} > 0

, if

n

is even then

u < 0

or

u > 0

2 x - 1 < 0 or 2 x - 1 > 0

2 x - 1 < 0 : x < \frac{1}{2}

2 x - 1 > 0 : x > \frac{1}{2}

Combine the intervals

x < \frac{1}{2} or x > \frac{1}{2}

Popular Examples

4 x - 1 \leq 7

2 x^{3} - x^{2} < 7 - 14 x

simplify 5/3-7/3 simplify

\frac{5}{3} - \frac{7}{3}

factor-x^3+4x^2-3x factor

- x^{3} + 4 x^{2} - 3 x

6 x^{2} + 4 x - 7 = 0

Frequently Asked Questions (FAQ)

What is 4x^2+1>4x ?
The solution to 4x^2+1>4x is x< 1/2 \lor x> 1/2