What is -5((x+1)/5)(x-5)>0 ?

The solution to -5((x+1)/5)(x-5)>0 is -1<x<5

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-5((x+1)/5)(x-5)>0

- 5 (\frac{x + 1}{5}) (x - 5) > 0

- 1 < x < 5

Interval Notation

(- 1, 5)

Solution steps

- 5 \cdot \frac{x + 1}{5} (x - 5) > 0

Simplify

- 5 \cdot \frac{1}{5} : - 1

- 5 \cdot \frac{x + 1}{5} (x - 5) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- 5 \cdot \frac{x + 1}{5} (x - 5)) (- 1) < 0 \cdot (- 1)

Simplify

(- 5 \cdot \frac{x + 1}{5} (x - 5)) (- 1) : (x + 1) (x - 5)

(x + 1) (x - 5) < 0

Identify the intervals

- 1 < x < 5

(10 x - 7) (x - 5) \leq 0

- 3 x^{2} + 7 x + 6 > 0

2 x^{2} - x - 6 < 14

\frac{1}{( x ^{2} )} < 2

x (x - 3) (x - 1)^{2} < 0