What is (x-3)>(x-3)(x-4) ?

The solution to (x-3)>(x-3)(x-4) is 3<x<5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x-3)>(x-3)(x-4)

(x - 3) > (x - 3) (x - 4)

3 < x < 5

Interval Notation

(3, 5)

Solution steps

x - 3 > (x - 3) (x - 4)

Rewrite in standard form

8 x - 15 - x^{2} > 0

Factor

8 x - 15 - x^{2} : - (x - 3) (x - 5)

- (x - 3) (x - 5) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3) (x - 5)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3) (x - 5) < 0

Identify the intervals

3 < x < 5

\frac{3}{5 x - 1} > 2 - x

24 x^{4} + 2 x^{3} - 5 x^{2} - x \geq 0

4 x^{3} - 9 x^{2} - 11 x + 26 \geq 0

x^{2} + x + 3 < 0

\frac{1}{( 4 x - 1 )} > 2