The solution to -x^2-15>8x is -5<x<-3

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-x^2-15>8x

Solution

- x^{2} - 15 > 8 x

- 5 < x < - 3

Interval Notation

(- 5, - 3)

Solution steps

- x^{2} - 15 > 8 x

Rewrite in standard form

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

Factor

- x^{2} - 15 - 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

- 5 < x < - 3

5 x^{2} - 13 x + 6

∣ 3 x - 4 ∣ \leq ∣ x + 4 ∣

1 0^{\frac{3}{2}}

m^{2} + 10 m + 5 = - 11

\frac{m}{8} = \frac{15}{24}