The solution to 5x-x^2>4 is 1<x<4

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5x-x^2>4

Solution

5 x - x^{2} > 4

1 < x < 4

Interval Notation

(1, 4)

Solution steps

5 x - x^{2} > 4

Rewrite in standard form

5 x - x^{2} - 4 > 0

Factor

5 x - x^{2} - 4 : - (x - 1) (x - 4)

- (x - 1) (x - 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (x - 4)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 1) (x - 4) < 0

Identify the intervals

1 < x < 4

\frac{x ^{2} + x + 3}{2 x ^{2} + x - 6} \geq 0

16 x^{2} + 4 = 0

5 - 2 \cdot ∣ 1 + 3 x ∣ \leq - 3

∣ 3 x - 4 ∣ + 2 = 1

- 5.3 = \frac{x}{5} + 7.2