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Popular >

2x+5<x^2-2x-16

Solution

2 x + 5 < x^{2} - 2 x - 16

Solution

x < - 3 or x > 7

+1

Interval Notation

(- \infty, - 3) \cup (7, \infty)

Solution steps

2 x + 5 < x^{2} - 2 x - 16

Rewrite in standard form

4 x + 21 - x^{2} < 0

Factor

4 x + 21 - x^{2} : - (x + 3) (x - 7)

- (x + 3) (x - 7) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x + 3) (x - 7)) (- 1) > 0 \cdot (- 1)

Simplify

(x + 3) (x - 7) > 0

Identify the intervals

x < - 3 or x > 7

Graph

Popular Examples

(3x-1)(x+5)-1<= 3(x-2)+21x

(3 x - 1) (x + 5) - 1 \leq 3 (x - 2) + 21 x

\frac{4}{( 3 x - 2 )} \leq - 2

3 x^{2} - 8 < - 2 x

((x-1)(x-2)^3(x-4)^2)/(x+3)>= 0

\frac{( x - 1 ) ( x - 2 ) ^{3} ( x - 4 ) ^{2}}{x + 3} \geq 0

x^{3} + 5 x^{2} + 4 x > 0

Frequently Asked Questions (FAQ)

What is 2x+5<x^2-2x-16 ?
The solution to 2x+5<x^2-2x-16 is x<-3\lor x>7