-15-x^2<8x

Solution

- 15 - x^{2} < 8 x

x < - 5 or x > - 3

Interval Notation

(- \infty, - 5) \cup (- 3, \infty)

Solution steps

- 15 - x^{2} < 8 x

Rewrite in standard form

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

Factor

- 15 - x^{2} - 8 x : - (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

x < - 5 or x > - 3

y^{2} + 8 y + 7

\frac{2 ( x + 1 )}{3} > x + 5

4 x^{2} = 2 x + 1

1 1^{2} + x^{2} = 1 2^{2}

- 3 x + 4 \geq 58